We present the results of the measurement of complex dielectric permittivity, in the microwave frequency region, on glass reinforced polybutylene terephthalate (PBT) with blue inorganic pigments. The cavity resonant method had been used in order to measure the shift in the resonant frequency of the cavity, caused by the insertion of a sample, which can be related to the real part of the complex permittivity. Also, the quality factor of the cavity decreases with the insertion of a sample. The changes in the inverse of this quality factor give the imaginary part. In order to predict the dielectric behavior of this composite, we had developed a program of numerical simulation to calculate the complex permittivity of the inclusion. By using some of dielectric mixture laws (Maxwell-Wagner-Sillars, Hanai, Looyenga, inverse and direct Wiener, and Bruggemann), we can predict the dielectric behavior of the composite in a large range of volume fraction of inclusions.