Fabry-Perot (F-P) resonators were built from two superconductive YBa2Cu3O7-δ (YBCO) films separated by a spacer. Each film of 35 nm thickness was deposited on a Si substrate ≈0.2 mm thick. A slow-scan Michelson interferometer was employed to measure the transmittance of the resonator in the far-infrared frequency region from 10 to 90 cm−1 at temperatures between 10 and 300 K. Measurements showed that in the normal state the peak (or resonant) transmittance decreases with temperature, whereas in the superconducting state it can increase with decreasing temperature. The transmittance of the resonator was calculated using properties of individual reflectors obtained previously. When the effect of partial coherence is taken into consideration, the calculated transmittance is in good agreement with the experiments. Furthermore, the maximum possible resonant transmittance was predicted based on an optimization analysis considering the interference effects. The effect of the YBCO film thickness on the transmittance peaks was also studied, showing that the resonant transmittance decreases but the finesse increases as the film thickness is increased. This study should help improve the future design of F-P resonators based on HTSC thin films.