Abstract: A whispering gallery resonator constructed from a ring of dielectric material that is enclosed in a conducting cylindrical enclosure having a top and bottom. The dimensions of the dielectric ring and the enclosure are chosen such that any additional resonant frequencies of the resonator are at frequencies sufficiently different from the first resonant frequency to allow the resonator to be used in a free-running oscillator. In one embodiment of the present invention, material is removed from the dielectric ring at locations spaced equally around the ring to move the frequency of one of two degenerate modes. In a second embodiment of the present invention, the dimensions are chosen such that the resonator has a second resonant frequency which is also far from any spurious modes. In this embodiment, the dielectric ring is constructed from a material having first and second dielectric constants depending on the direction of polarization of electromagnetic waves in the material.