Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statement on Form S-8 of Adagio Medical Holdings, Inc. (the “Company”) of our report dated March 26, 2025, relating to the consolidated financial statements of the Company as of December 31, 2025 and 2024 and for the years then ended, which includes an explanatory paragraph relating to the Company’s ability to continue as a going concern, appearing in the Company’s Annual Report on Form 10-K for the years ended December 31, 2025 and 2024.

/s/ WithumSmith+Brown, PC

Whippany, New Jersey

March 27, 2026