In this work we study the unique problems associated with resolving the direction of arrival (DOA) of coherent signals separated by less than an antenna beamwidth when the data are collected in the beamspace domain with, for example, electronically or holographically scanned antennas. We also propose a technique that is able to resolve these coherent signals. The technique is based on interpolation of the data measured by an element-space virtual array. Although the data are collected in the beamspace domain, the coherence structure can be broken by interpolating multiple shifted element-space virtual arrays. The efficacy of this technique depends on a fundamental tradeoff that arises due to a nonuniform signal-to-noise ratio (SNR) profile across the elements of the virtual array. This profile is due to the structure imposed by the specific beam pattern of the antenna. In addition to describing our technique and studying the SNR profile tradeoff, we also incorporate a strategy for improving performance through a subswath technique that improves covergence of covariance estimates.