A rigorous mode-matching technique is implemented for the study of the unloaded Q factor of a dielectric resonator operating in the TE01delta, TM01delta, and HEM11deltamodes. The cylindrical dielectric resonator is loaded into a metal enclosure and placed on a dielectric substrate. The analysis permits the calculation of the loss introduced by the resonator parameters and also the electromagnetic energy distribution inside the cavity. Numerical results are presented demonstrating the variation of the unloaded Q factor, electromagnetic energy distribution, and power loss against geometrical and material parameters. Finally, the accuracy of the calculations is verified with comparison with another rigorous method.