A system was developed to measure the microwave power dependence of the surface resistance superconductor films. The system uses a dielectric resonator method combined with a circle fit technique and a two-mode technique to measure the microwave surface resistance of superconductor films. For validation, this system was used to measure such surface resistance for superconductor films with different surface morphologies. Significant difference in microwave power dependence of surface resistance was observed. This measurement system proved suitable for evaluating superconducting films for passive microwave devices, including high power devices such as transmitting filters.