Herein we present an optical cavity in the form of a prolate ellipsoid that can greatly enhance the performance of solar thermophotovoltaic (STPV) systems. The geometrical parameters of the cavity can be designed to control the degree of photon recycling, the temperature of the emitter within the STPV system, gap distance and effective view factor between the PV cell and the emitter, and to minimize the emission losses. Numerical analysis shows the ellipsoidal optical cavity can be designed to achieve an effective view factor of 88.7% between the emitter and PV cell within a STPV system. Results show an efficiency of 5.62% in a STPV system with a GaSb PV cell and a black-body emitter under solar radiation at a concentration factor of 350X. Further, assuming the surface of the ellipsoidal optical cavity is capable of reflecting 99% of the radiation incident onto its surface, efficiencies of 15.54% can be attained when the solar concentration factor is 1400X. These results are attained for STPV systems without using selective absorbers, emitters or filters. The ellipsoidal optical cavity can be integrated into the design of advanced TPV systems and bring them closer to the high theoretical efficiencies TPV systems are capable of.