Exhibit 32.1

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CERTIFICATION OF CHIEF EXECUTIVE OFFICER PURSUANT TO SECTION 906 OF
THE SARBANES-OXLEY ACT OF 2002 (SUBSECTIONS (a) AND (b)
OF SECTION 1350, CHAPTER 63 OF TITLE 18, UNITED STATES CODE)

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Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code), I, William A. Zartler, Chairman and Co-Chief Executive Officer of Solaris Energy Infrastructure, Inc. (the “Company”), hereby certify, to my knowledge, that:

(1)the Company’s Quarterly Report on Form 10-Q for the quarter ended September 30, 2025 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

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