In this paper the fundamental effects of losses on resonant parameters (frequencies and quality factors) are analyzed for circular-cylindrical dielectric resonators inserted between metal plates, in the configuration also called NRD (Non-Radiative Dielectric). Power dissipations are considered both in the dielectric and in the conductors. Complex resonant frequencies and closed-form expressions for the relevant quality factors are derived rigorously for arbitrary resonant modes, even without circular symmetry. Numerical results are presented and discussed, making also use of experimental data obtained by means of a suitable NRD set-up. The present analysis accurately provides the basic information for a more realistic design of up-to-date millimeter-wave frequency-selective devices in NRD circuitry.