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We measure the thickness of YBa2Cu3O 7−δ (YBCO) films at a microwave frequency of 39.91 GHz noninvasively by using the single two-resonance-mode sapphire resonator (TSR) method. In the TSR method, a single sapphire resonator is used for measuring the effective surface resistance (R S,eff) and the penetration depth (λ) of the YBCO films at the same frequency at temperatures of 6-88 K. Five YBCO films having thicknesses of 70-360 nm are used in this study. The thickness, t(RF), of the YBCO films as measured at 10, 30, 50, and 77 K by using the TSR method turns out to be almost the same as the corresponding one, t(step), as measured by using step profilometry. The differences between t(RF) and t(step) appear to be less than ∼5% regardless of the film thickness and the measured temperature, which is smaller than the corresponding value of ∼7% as observed by using the two-resonance-mode rutile resonator (TRR) method. The differences between the average t(RF) of each YBCO film and the corresponding t(step) turn out to be less than ∼3% in both methods. We discuss the merits in using the TSR method in relation with the TRR method. Our study shows that the TSR method could be very useful for noninvasive measurements of the thicknesses of various superconductor films with accuracy by using microwaves.