Abstract: A simplified apparatus and a design method for providing microwave resonators having high Q factors. The apparatus includes a resonant microwave cavity having three mutually orthogonal dimensions and a low loss dielectric body substantially enclosing each dimension of the resonant microwave cavity. To further increase Q-factor, the apparatus of the invention preferably includes a plurality of resonant microwave cavities and a plurality of low loss dielectric bodies each substantially enclosing a respective one of the microwave resonant cavities. In some embodiments the low loss dielectric bodies are arranged in a stack. In other embodiments the low loss dielectric bodies are concentrically arranged.