We examine the problem of interpolating antenna radiation patterns from a small number of measurements and propose an algorithm to perform the interpolation when naive methods fail, often due to multipath corruption of the pattern. This algorithm exploits constraints on the antenna's underlying design to avoid ambiguities but is sufficiently general to address many different antenna types. A theoretical basis for the robustness of this algorithm is developed, and its performance is verified in simulation using a number of popular antenna designs and with a controlled laboratory experiment.