tw telecom 10-Q 2013 Q3 Quarterly report

Exhibit 32.1

Certification of Chief Executive Officer

Pursuant to 18 U.S.C. 1350

(as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002)

In connection with the Quarterly Report of tw telecom inc. (the “Company”) on Form 10-Q for the period ended September 30, 2013 filed with the Securities and Exchange Commission (the “Report”), I, Larissa L. Herda, Chairman, President and Chief Executive Officer 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 (15 U.S.C. Section 78m or 78o(d)); and

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

/s/ Larissa L. Herda

Name: Larissa L. Herda

Date: November 6, 2013