This thesis develops a method for obtaining the complex resonant frequency of a post dielectric resonator in the presence of a lossy conductor. A full field analysis is performed on an infinite dielectric rod from which the complex propagation constant and modal solutions are found. Using a single dominant mode (HEM_ll), the boundary conditions at the end of the resonator are enforced, to obtain a complex reflection coefficient. Using the propagation constant from the infinite dielectric rod and the reflection coefficient derived from considering the dielectric-air interface at the resonator ends, a two dimensional search is performed to find the complex frequency for which the gain/phase criterion of the resonator is satisfied. In the final step, boundary conditions are enforced for a lossy conductor at a distance Az from the dielectric which yields the objective -- the complex resonate frequency of a post dielectric in close proximity of a lossy conductor / Master of Science