This research is directed towards developing suitable measurement methods and related computer software for nondestructive characterization of the complex permittivity of materials at UHF and microwave frequencies. An open-ended coaxial line will be used to make permittivity measurements. A stationary variational formulation for the aperture impedance of the coaxial opening on a ground plane will be used to relate its input reflection coefficient with the electrical properties of the sample medium. To start with, large sample media will be considered. Thin dielectric sheet materials will be considered later. The fourier transform method will be used to solve the case of thin dielectric sheet materials, and possibilities of the surface wave excitation will be considered.