EXHIBIT 32.1

CERTIFICATION BY KEVIN J. MCNAMARA

PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, as President and Chief Executive Officer of Chemed Corporation (“Company”), does hereby certify that:

1)The Company’s Annual Report on Form 10-K for the year ending December 31, 2023 (“Report”), 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.

Dated: February 29, 2024

/s/ Kevin J. McNamara

Kevin J. McNamara

(President and Chief Executive Officer)