Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the following Registration Statements:

(1)Registration Statement (Form S-3 Nos. 333-276793, 333-273949 and 333-271115) of CalciMedica, Inc. (formerly Graybug Vision, Inc.),

(2) Registration Statement (Form S-8 No. 333-271898) pertaining to the Amended and Restated 2006 Stock Plan, 2023 Equity Incentive Plan, and 2023 Employee Stock Purchase Plan of CalciMedica, Inc. (formerly Graybug Vision, Inc.),

(3) Registration Statement (Form S-8 No. 333-249033) pertaining to the 2020 Equity Incentive Plan, 2020 Employee Stock Purchase Plan and 2015 Stock Incentive Plan of CalciMedica, Inc. (formerly Graybug Vision, Inc.),

(4) Registration Statement (Form S-8 No. 333-254522) pertaining to the 2020 Equity Incentive Plan of CalciMedica, Inc. (formerly Graybug Vision, Inc.),

(5) Registration Statement (Form S-8 No. 333-263464) pertaining to the 2020 Equity Incentive Plan and certain inducement grants of CalciMedica, Inc. (formerly Graybug Vision, Inc.), and

(6) Registration Statement (Form S-8 No. 333-266980) pertaining to the Amended and Restated 2020 Equity Incentive Plan of CalciMedica, Inc. (formerly Graybug Vision, Inc.);

of our report dated March 28, 2024, with respect to the consolidated financial statements of CalciMedica, Inc. included in this Annual Report (Form 10-K) of CalciMedica, Inc. for the year ended December 31, 2023.

/s/ Ernst & Young LLP

San Diego, California

March 28, 2024