Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statements on Form S-3 (No. 333-276793, No. 333-273949 and No. 333-271115) and Form S-8 (No. 333-281800, No. 333-278336, No. 333-271898, No. 333-266980, No. 333-263464, No. 333-263464, No. 333-254522 and No. 333-249033) of CalciMedica, Inc. (the “Company”), of our report dated March 27, 2025, relating to the consolidated financial statements as of and for the year ended December 31, 2024 of the Company (which report expresses an unqualified opinion), appearing in this Annual Report on Form 10-K of the Company for the year ended December 31, 2024.

/s/ Moss Adams LLP

San Diego, California

March 27, 2025