Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption “Experts” in the Registration Statement (Form S-3) and related Prospectus of CalciMedica, Inc. (formerly Graybug Vision, Inc.) for the registration of up to $100,000,000 of its common stock, preferred stock, debt securities and warrants and to the incorporation by reference therein of our report dated March 8, 2023, with respect to the consolidated financial statements of CalciMedica, Inc. (formerly Graybug Vision, Inc.) included in its Annual Report (Form 10-K) for the year ended December 31, 2022, as amended on April 4, 2023 by Amendment No. 1 on Form 10-K/A, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

San Mateo, California

August 11, 2023