EXHIBIT 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO SECTION 906 OF

THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of West Pharmaceutical Services, Inc. (the “Company”) for the period ended March 31, 2024, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Eric M. Green, President and Chief Executive Officer, Chair of the Board of Directors of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

/s/ Eric M. Green

Eric M. Green

President and Chief Executive Officer, Chair of the Board of Directors

Date: April 25, 2024