An important barrier to the application of high-temperature superconducting microwave filters is their power-handling capability. To clarify the key parameters for improving the power-handling capability of rf filters based on high-temperature superconductors with microstrip structures, we synthesize bandpass filters with different layouts using several kinds of thin film high-temperature superconductors, and subject them to third-order intermodulation measurements. By improving the sensitivity of the measurement set-up through the selective reduction of the fundamental output signals, we succeed in measuring the intermodulation signals of the superconducting filters. The experimental results indicate that increasing the film thickness and utilizing MBE-grown films of NdBa2Cu3O7 films are effective in obtaining high-power handling microstrip filters.