Exhibit 32.1

Certification of Principal Executive Officer

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, I, Peter Altman, the President and Chief Executive Officer of BioCardia, Inc. (the "Company"), hereby certify, that, to my knowledge:

1.     The Annual Report on Form 10-K for the year ended December 31, 2018 (the "Report") of the Company fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2.     The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: April 1, 2019

/s/ Peter Altman

Name: Peter Altman

Title: President and Chief Executive Officer