Exhibit 23.1 

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Prospectus constituting a part of this Registration Statement on Form S-8 of our report dated March 27, 2025, which includes an explanatory paragraph regarding Adagio Medical Holdings, Inc.’s ability to continue as a going concern, relating to the consolidated financial statements of Adagio Medical Holdings, Inc. as of and for the years ended December 31, 2024 and 2023, which is contained in that Prospectus. We also consent to the reference to our Firm under the caption “Experts” in the Prospectus.

/s/ WithumSmith+Brown, PC

Whippany, New Jersey

March 27, 2025