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The return loss (reflection coefficient) of a paraboloidal reflector antenna covered by a paraboloidal radome is predicted using a physical-optics method based on the power-coupling theorem. An asymptotic form of the expression is found to be a good approximation. The performance of the antenna has been measured and results are in good agreement with those predicted theoretically. A method for reducing the return loss is investigated using a hemispherical iris-loaded sandwich section at the center of the radome. An improvement in return loss of approximately 5 dB is observed over a useful frequency bandwidth. Contributions of the radome to the radiation pattern of the antenna have been identified and those near to boresight have been predicted. Computed values in that region agree well with measurements.