This work reports the microwave frequency dielectric properties of PBX 9501 and one of its representative mocks, PBS 9501, within 1-20 GHz. From these measurements it is shown that the binder system has a strong influence on microwave heating of such compositions resulting in significant temperature gradients within the individual HMX or sugar crystals at high microwave heating rates. Using the measured dielectric properties, COMSOL 4.3 Multiphysics was used to simulate and optimize a microwave applicator with a high electric field to input power ratio. The simulated applicator design indicated subsecond heating to decomposition for PBX 9501 and was validated with small scale experiments on both PBS 9501 and PBX 9501. At approximately 2.45 GHz and 100 W applied power, PBS 9501 decomposition was observed shortly (< 34 ms) after a measured surface temperature of 70 °C (binder system melts). Finally, rapid heating of PBX 9501 was also shown in the optimized cavity.