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. 333-288287, No. 333-281800, No. 333-278336, and No. 333-271898) of CalciMedica, Inc. (the “Company”) of our report dated March 3, 2026, relating to the consolidated financial statements of the Company (which report expresses an unqualified opinion and includes an explanatory paragraph relating to a going concern uncertainty), appearing in this Annual Report on Form 10-K of the Company for the year ended December 31, 2025.

/s/ Baker Tilly US, LLP

San Diego, California

March 3, 2026