Exhibit 32.1

CERTIFICATION OF PRINCIPAL EXECUTIVE OFFICER PURSUANT TO

18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Adagio Medical Holdings, Inc. (formerly known as “Aja Holdco, Inc.”) (the “Company”) for the quarter ended September 30, 2024 as filed with the Securities and Exchange Commission on the date hereof (the “Quarterly Report”), I, Olav Bergheim, Chief Executive Officer (Principal Executive Officer) of the Company, hereby certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

1. The Quarterly Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

Date: November 14, 2024	By:	/s/ Olav Bergheim
		Olav Bergheim
		Chief Executive Officer
		(Principal Executive Officer)