A theoretical analysis and measurement technique to determine the complex permittivity and permeability of cylindrical and ring type dielectric resonators is given. The resonant frequency, unloaded quality factor and physical dimensions of dielectric resonator placed between two parallel conducting plates are used to evaluate the complex permittivity and permeability. This process is repeated for other higher-order modes to expand the evaluation at higher resonant frequencies. The nature of each mode is identified by measuring the variations of field strength along the azimuthal and longitudinal direction. An error analysis taking into account various error sources reveals that $TE_{0np}$ or quasi-TE modes yield the least amount of measurement error, which is less than $0.5{\%}$for the real part, $4{\%}$for the imaginary part of complex permittivity.