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

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (“Section 906”), C. Robert Udell Jr. and Fred A. Graffam III, President and Chief Executive Officer and Chief Financial Officer, respectively, of Consolidated Communications Holdings, Inc., each certify that to his knowledge (i) the Quarterly Report on Form 10-Q for the period ended September 30, 2023 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, and (ii) the information contained in such report fairly presents, in all material respects, the financial condition and results of operations of Consolidated Communications Holdings, Inc.

/s/ C. Robert Udell Jr.

C. Robert Udell Jr.

President and Chief Executive Officer

(Principal Executive Officer)

November 7, 2023

/s/ Fred A. Graffam III

Fred A. Graffam III

Chief Financial Officer

(Principal Financial Officer and Principal Accounting Officer)

November 7, 2023

The foregoing certifications shall not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”) or otherwise subject to the liabilities of that section, nor shall it be deemed to be incorporated by reference in any registration statement or other document filed under the Securities Act of 1933, as amended or the Exchange Act, except as expressly set forth by reference in such a filing.