We aim to understand how microwaves interact with high explosives by studying the complex permittivity from 1-18GHz of HMX, RDX, TNT, TATB, PETN, Octol, Comp B, 95% RDX/5% Viton A (PBX-RDX), PBX 9404, PBXN-5, PBXN-7, PBXW-14, PBX 9501, and PBX 9502. The combination of a resonant cavity perturbation technique for determining the room-temperature complex dielectric constant at discrete frequencies and a wide band open circuit method (1-18GHz) provides an accurate, broadband measurement that describes the dielectric properties in the frequency range of interest. While the values of the real and imaginary permittivity components did not vary significantly as a function of frequency, we found the real part of the permittivity to be highly dependent on relatively small changes in the material density. We used dielectric mixing theory, specifically the linear-law approximation, to compare the predicted values based on the dielectric properties of individual components with those of the resulting formulation measured experimentally for a select number of samples; the prediction agrees well within the observed variability of the experimentally measured values.