Spherical dielectric resonators are investigated as on-chip high-efficiency antenna and as on-chip high-Q resonator. A dielectric sphere of alumina ceramic is precisely placed atop the semiconductor in a shallow crate etched into the back-end-of-line dielectric layers on the chip surface. The sphere resonates in a higher-order mode, efficiently coupled to the on-chip planar microstrip excitation structure. For sphere diameter of 1.1 mm, an antenna with gain of 5.1 dBi and efficiency of 33% is demonstrated at 100 GHz. For a sphere diameter of 1 mm, a resonator is demonstrated with measured loaded Q-factor of 143 at 103 GHz.