Exhibit 32.1—CERTIFICATION OF CHIEF EXECUTIVE OFFICER PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the quarterly report of Luna Innovations Incorporated (the “Company”) on Form 10-Q for the period ending September 30, 2006 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Kent A. Murphy, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that to my knowledge:

(1) The 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.

/s/    KENT A. MURPHY        

Kent A. Murphy, Ph.D.

President and Chief Executive Officer

November 13, 2006