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 Annual Report on Form 10-K for the fiscal year ended December 31, 2022 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)

March 3, 2023

/s/ Fred A. Graffam III

Fred A. Graffam III

Chief Financial Officer
(Principal Financial Officer and Chief Accounting Officer)

March 3, 2023

The foregoing certifications are not deemed filed with the Securities and Exchange Commission for purposes of Section 18 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”) and are not to be incorporated by reference into any filing of Consolidated Communications Holdings, Inc. under the Securities Act of 1933, as amended, or the Exchange Act, whether made before or after the date hereof, regardless of any general incorporation language contained in such filing.