Exhibit 4.2

FORM OF WARRANT CERTIFICATE

THE WARRANT AND THE SECURITIES ISSUABLE UPON EXERCISE OF THIS WARRANT, HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), OR THE SECURITIES LAWS OF ANY STATE OR OTHER JURISDICTION. THE SECURITIES MAY NOT BE OFFERED, SOLD, PLEDGED, HYPOTHECATED, OR OTHERWISE TRANSFERRED EXCEPT (1) PURSUANT TO AN EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OR (2) PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT, IN EACH CASE IN ACCORDANCE WITH ALL APPLICABLE STATE SECURITIES LAWS AND THE SECURITIES LAWS OF OTHER JURISDICTIONS, AND, IF REQUESTED BY THE COMPANY, UPON DELIVERY OF AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH TRANSFER IS EXEMPT FROM REGISTRATION.

UNLESS PERMITTED UNDER SECURITIES LEGISLATION, THE HOLDER OF THIS SECURITY MUST NOT TRADE THE SECURITY BEFORE [THE DATE THAT IS FOUR MONTHS AND ONE DAY FROM THE CLOSING DATE].

THE SECURITIES ISSUABLE UPON THE EXERCISE OF THIS WARRANT CERTIFICATE ARE LISTED ON THE TORONTO STOCK EXCHANGE (“TSX”); HOWEVER, THE SAID SECURITIES CANNOT BE TRADED THROUGH THE FACILITIES OF TSX SINCE THEY ARE NOT FREELY TRANSFERABLE, AND CONSEQUENTLY ANY CERTIFICATE REPRESENTING SUCH SECURITIES IS NOT “GOOD DELIVERY” IN SETTLEMENT OF TRANSACTIONS ON TSX.

Warrant Certificate No.: ■

Original Issue Date: October ■, 2025

FOR VALUE RECEIVED, Perpetua Resources Corp., a company incorporated under the Business Corporations Act (British Columbia) (the “Company”), hereby certifies that [·], a [·] (the “Holder”) is entitled to purchase from the Company ■ Common Shares (as defined below) at an exercise price per share of $■ (subject to adjustment as provided herein, the “Exercise Price”), all subject to the terms, conditions, and adjustments set forth in this Warrant. Certain capitalized terms used herein are defined in Section ‎1.

1.            Definitions. As used in this Warrant, the following terms have the respective meanings set forth below:

provided, however, if the Common Shares are not then listed on any such exchange or market, the Current Market Price shall be determined by a firm of independent chartered accountants selected by the directors of the Company, acting reasonably and in good faith.

2.            Term of Warrant. Subject to the terms and conditions hereof, at any time or from time to time after the date hereof, and at or prior to 5:00 p.m. (New York City time) (the “Expiry Time”), on the Expiry Date (the “Exercise Period”), the Holder of this Warrant may exercise this Warrant for all or any part of the Warrant Shares purchasable hereunder (subject to adjustment as provided herein).

3.            Exercise of Warrant.

4.            Redemption.

5.            Adjustment to Exercise Price and Number of Warrant Shares. The Exercise Price and the number of Warrant Shares issuable upon exercise of this Warrant shall be subject to adjustment from time to time as provided in this Section ‎4 (in each case, after taking into consideration any prior adjustments pursuant to this Section ‎4).

then the Exercise Price in effect on the effective date or record date of any such Common Share Reorganization shall be adjusted immediately after such event, or on the record date for such Common Share Reorganization, as the case may be, so that it shall equal the amount determined by multiplying the Exercise Price in effect immediately prior to such event or record date, by a fraction: (A) the numerator of which shall be the total number of Common Shares outstanding immediately prior to giving effect to such Common Share Reorganization; and (B) the denominator of which shall be the total number of Common Shares outstanding immediately after giving effect to such Common Share Reorganization (including, in the case where securities exchangeable for or convertible into Common Shares are distributed, the number of Common Shares that would have been outstanding had all such securities been exchanged for or converted into Common Shares on such effective date or record date, as the case may be).

To the extent that any such securities are not so issued or exercised prior to the expiration thereof, the Exercise Price shall then be re-adjusted to the Exercise Price which would then be in effect based upon the number of Common Shares actually issued and remaining issuable after such expiration, and will be further re-adjusted in such manner upon expiration of any further such securities.

To the extent that any such rights, options or warrants are not so issued or exercised prior to the expiration thereof, the Exercise Price shall then be re-adjusted to the Exercise Price which would then be in effect based on the aggregate price of the total number of Common Shares (or the aggregate conversion or exchange price of the convertible or exchangeable securities) actually issued and remaining issuable upon the exercise of such convertible or exchangeable securities, as the case may be.

If by the terms of the rights, options or warrants referred to in this Section 5(b), there is more than one purchase, conversion or exchange price per Common Share, the aggregate price of the total number of additional Common Shares offered for subscription or purchase, or the aggregate conversion or exchange price of the convertible securities so offered, shall be calculated for purposes of the adjustment on the basis of the lowest purchase, conversion or exchange price per Common Share, as the case may be.

To the extent that such distribution is not so made, the Exercise Price shall be re-adjusted to the Exercise Price which would then be in effect if such record date had not been fixed or to the Exercise Price which would then be in effect based upon such securities, rights, options, warrants, evidences of indebtedness or other property or assets actually distributed, as the case may be.

(f)            Adjustment Rules.

(g)            Notices. In the event:

then, and in each such case, to the extent practicable, the Company shall send or cause to be sent to the Holder at least 5 Business Days prior to the applicable record date or the applicable expected effective date, as the case may be, for the event, a written notice specifying, as the case may be: (A) the record date for such dividend, distribution, meeting or consent, or other right or action, and a description of such dividend, distribution, or other right or action to be taken at such meeting or by written consent; or (B) the effective date on which such reorganization, reclassification, consolidation, merger, sale, dissolution, liquidation, or winding-up is proposed to take place, and the date, if any is to be fixed, as of which the books of the Company shall close or a record shall be taken with respect to which holders of record of Common Shares (or such other capital shares or securities at the time issuable upon exercise of the Warrant) shall be entitled to exchange their Common Shares (or such other capital shares or securities) for securities or other property deliverable upon such reorganization, reclassification, consolidation, merger, sale, dissolution, liquidation, or winding-up, and the amount per share and character of such exchange applicable to the Warrant and the Warrant Shares; provided, however, that the Company may satisfy this Section ‎5(g) by publicly disclosing such information in a document filed or furnished with the Commission or a widely distributed press release, in each case, on or prior to the applicable notice deadline set forth herein.

6.            Transfer of Warrant. This Warrant and the rights hereunder are not transferable except that the Holder may transfer this Warrant, in whole or in part, to any affiliate of the Holder that is controlled by the Holder, upon delivery or surrender of this Warrant to the Company electronically or at its then principal executive offices with a properly completed and duly executed assignment in the form attached hereto as Exhibit B. To the extent any transfer or withholding taxes are payable in connection with such transfer, the Holder shall be responsible for any such taxes. Upon satisfaction of the foregoing procedures, the Company shall execute and deliver a new warrant certificate in respect of this Warrant in the name of the assignee or assignees and in the denominations specified in such instrument of assignment, and shall issue to the assignor a new warrant certificate evidencing the portion of this Warrant, if any, not so assigned and this Warrant shall promptly thereafter be and be deemed to be cancelled.

7.            Holder Not Deemed a Shareholder; Limitations on Liability. Except as otherwise specifically provided herein, prior to the issuance to the Holder of the Warrant Shares to which the Holder is then entitled to receive upon the due exercise of this Warrant, the Holder shall not be entitled solely by virtue of holding this Warrant to vote or receive dividends or be deemed the holder of shares of the Company for any purpose, nor shall anything contained in this Warrant be construed to confer upon the Holder, as such, any right to vote, give, or withhold consent to any corporate action (whether any reorganization, issue of shares, reclassification of shares, consolidation, merger, conveyance, or otherwise), receive notice of meetings, receive dividends or subscription rights, or otherwise. In addition, nothing contained in this Warrant shall be construed as imposing any liabilities on the Holder to purchase any securities (upon exercise of this Warrant or otherwise) or as a shareholder of the Company whether such liabilities are asserted by the Company or by creditors of the Company.

8.            Replacement on Loss; Division and Combination.

9.            Compliance with the Securities Act.

THIS WARRANT AND THE SECURITIES ISSUABLE UPON EXERCISE OF THIS WARRANT, HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), OR THE SECURITIES LAWS OF ANY STATE OR OTHER JURISDICTION. THE SHARES MAY NOT BE OFFERED, SOLD, PLEDGED, HYPOTHECATED, OR OTHERWISE TRANSFERRED EXCEPT (1) PURSUANT TO AN EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OR (2) PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT, IN EACH CASE IN ACCORDANCE WITH ALL APPLICABLE STATE SECURITIES LAWS AND THE SECURITIES LAWS OF OTHER JURISDICTIONS, AND, IF REQUESTED BY THE COMPANY, UPON DELIVERY OF AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH TRANSFER IS EXEMPT FROM REGISTRATION.

UNLESS PERMITTED UNDER SECURITIES LEGISLATION, THE HOLDER OF THIS SECURITY MUST NOT TRADE THE SECURITY BEFORE [THE DATE THAT IS FOUR MONTHS AND ONE DAY FROM THE CLOSING DATE].

THE [SECURITIES ISSUABLE UPON THE EXERCISE OF THE] SECURITES REPRESENTED BY THIS CERTIFICATE ARE LISTED ON THE TORONTO STOCK EXCHANGE (“TSX”); HOWEVER, THE SAID SECURITIES CANNOT BE TRADED THROUGH THE FACILITIES OF TSX SINCE THEY ARE NOT FREELY TRANSFERABLE, AND CONSEQUENTLY ANY CERTIFICATE REPRESENTING SUCH SECURITIES IS NOT “GOOD DELIVERY” IN SETTLEMENT OF TRANSACTIONS ON TSX.

10.            Warrant Register. The Company shall keep and properly maintain at its principal executive offices books for the registration of the Warrant and any transfers thereof.

11.            Notices. All notices (including any Exercise Notice), requests, consents, claims, demands, waivers, and other communications hereunder shall be in writing and shall be deemed to have been given: (a) when delivered by hand; (b) when received by the addressee if sent by a nationally recognized overnight courier; (c) on the date sent by email if sent prior to 5:00 p.m. on a Business Day (New York City time) or on the next Business Day if sent after 5:00 p.m. (New York City time) on a Business Day or on any day that is not a Business Day; or (d) on the third day after the date mailed, by certified or registered mail. Such communications must be sent to the respective parties at the addresses indicated below (or at such other address as shall be specified in a notice given in accordance with this Section ‎11).

12.            Cumulative Remedies. Except to the extent expressly provided in Section ‎7 to the contrary, the rights and remedies provided in this Warrant are cumulative and are not exclusive of, and are in addition to and not in substitution for, any other rights or remedies available at law, in equity or otherwise.

13.            Entire Agreement. This Warrant, together with the Subscription Agreement and the Registration Rights Agreement, constitutes the sole and entire agreement of the parties with respect to the subject matter contained herein, and supersedes all prior and contemporaneous understandings and agreements, both written and oral, with respect to such subject matter. In the event of any inconsistency between the statements in the body of this Warrant and the statements in the Subscription Agreement or the Registration Rights Agreement, the statements in the body of this Warrant shall control.

14.            Successors and Assigns. This Warrant and the rights evidenced hereby shall be binding upon and shall inure to the benefit of the parties hereto and the successors of the Company and the successors and permitted assigns of the Holder. Such successors and/or permitted assigns of the Holder shall be deemed to be a Holder for all purposes hereunder.

15.            No Third-Party Beneficiaries. This Warrant is for the sole benefit of the Company and the Holder and their respective successors and, in the case of the Holder, permitted assigns and nothing herein, express or implied, is intended to or shall confer upon any other Person any legal or equitable right, benefit, or remedy of any nature whatsoever, under or by reason of this Warrant.

16.            Interpretation. For purposes of this Warrant and unless the context otherwise requires: (a) the words “include”, “includes”, and “including” are deemed to be followed by the words “without limitation”; (b) the word “or” is not exclusive; and (c) the words “herein”, “hereof”, “hereby”, “hereto”, and “hereunder” refer to this Warrant as a whole. All references to “$” means the lawful currency of the United States of America. Whenever the singular is used in this Warrant, the same shall include the plural, and whenever the plural is used herein, the same shall include the singular, where appropriate. The headings in this Warrant are for reference only and shall not affect the interpretation of this Warrant.

17.            Amendment and Modification; Waiver. Except as otherwise provided herein, this Warrant may only be amended, modified, or supplemented by an agreement in writing signed by each party hereto. No waiver by the Company or the Holder of any of the provisions hereof shall be effective unless explicitly set forth in writing and signed by the party so waiving. No waiver by any party shall operate or be construed as a waiver in respect of any failure, breach, or default not expressly identified by such written waiver, whether of a similar or different character, and whether occurring before or after that waiver. No failure to exercise, or delay in exercising, any rights, remedy, power, or privilege arising from this Warrant shall operate or be construed as a waiver thereof; nor shall any single or partial exercise of any right, remedy, power, or privilege hereunder preclude any other or further exercise thereof or the exercise of any other right, remedy, power, or privilege.

18.            Severability. If any term or provision of this Warrant is invalid, illegal, or unenforceable in any jurisdiction, such invalidity, illegality, or unenforceability shall not affect any other term or provision of this Warrant or invalidate or render unenforceable such term or provision in any other jurisdiction.

19.            Governing Law. This Warrant shall be governed by and construed in accordance with the internal laws of the State of New York without giving effect to any choice or conflict of law provision or rule (whether of the State of New York or any other jurisdiction) that would cause the application of laws of any jurisdiction other than those of the State of New York.

20.            Submission to Jurisdiction. Any legal suit, action, or proceeding arising out of or based upon this Warrant or the transactions contemplated hereby may be instituted in the federal courts of the United States of America or the courts of the State of New York in each case located in the city of New York and County of New York, and each party irrevocably submits to the exclusive jurisdiction of such courts in any such suit, action, or proceeding. Service of process, summons, notice, or other document by certified or registered mail to such party’s address set forth herein shall be effective service of process for any suit, action, or other proceeding brought in any such court. The parties irrevocably and unconditionally waive any objection to the laying of venue of any suit, action, or any proceeding in such courts and irrevocably waive and agree not to plead or claim in any such court that any such suit, action, or proceeding brought in any such court has been brought in an inconvenient forum.

21.            Waiver of Jury Trial. Each party acknowledges and agrees that any controversy which may arise under this Warrant is likely to involve complicated and difficult issues and, therefore, each such party irrevocably and unconditionally waives any right it may have to a trial by jury in respect of any legal action arising out of or relating to this Warrant or the transactions contemplated hereby.

22.            No Strict Construction. This Warrant shall be construed without regard to any presumption or rule requiring construction or interpretation against the party drafting an instrument or causing any instrument to be drafted.

23.            Signature and Electronic Copies. This Warrant may be signed digitally or by other electronic means, which shall be deemed to be an original and shall be deemed to have the same legal effect and validity as a certificate bearing an original signature. A signed copy of this Warrant transmitted by email or other electronic transmission shall be deemed to have the same legal effect and validity as delivery of an originally executed copy of this Warrant.

[signature page follows]

IN WITNESS WHEREOF, the Company has duly executed and issued to the Holder this Warrant on the Original Issue Date.

Exhibit A

Exercise Notice

To:         PERPETUA RESOURCES CORP.

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Exhibit B

Assignment Form

(To assign the foregoing Warrant to an affiliate of Holder that is controlled by the Holder pursuant to Section 6 of the Warrant, execute this form and supply required information. Do not use this form to purchase shares or to transfer the Warrant or any Warrant Shares to a non-affiliate.)

NOW, THEREFORE, FOR VALUE RECEIVED, the attached Warrant and all rights evidenced thereby are hereby assigned to:

Exhibit C

Wire Transfer Instructions

(see attached)