Exhibit 32.1

Section 1350 Certification of the Plan's Chief Executive Officer

and Chief Financial Officer

In connection with the Annual Report on Form 11-K for the plan year ended December 31, 2018 (the "Report") of The 401(k) Stock Purchase Plan for Employees of Cullen/Frost Bankers, Inc. and its Affiliates (the "Plan") and pursuant to Subsections (a) and (b) of Section 1350 of Chapter 63 of Title 18 of the United States Code in accordance with Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, Annette Alonzo,Plan Administrator, Plan Chief Executive Officer and Plan Chief Financial Officer hereby certifies, to her knowledge, that the Report fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934, and the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Plan.

June 21, 2019

/s/ Annette Alonzo    

Annette Alonzo

The forgoing certification is being furnished solely pursuant to Subsections (a) and (b) of Section 1350 of Chapter 63 of Title 18 of the United States Code in accordance with Section 906 of the Sarbanes-Oxley Act of 2002 and shall not be deemed "filed" for purposes of Section 18 of the Securities Exchange Act of 1934, or otherwise subject to the liability of that section, and shall not be deemed to be incorporated by reference into any filing under the Securities Act of 1933 or the Securities Exchange Act of 1934.