Selective solar absorbers generally have limited effectiveness in unconcentrated sunlight, because of reradiation losses over a broad range of wavelengths and angles. However, metamaterials offer the potential to limit radiation exchange to a proscribed range of angles and wavelengths, which has the potential to dramatically boost performance. After globally optimizing one particular class of such designs, we find thermal transfer efficiencies of 78% at temperatures over 1,000°C, with overall system energy conversion efficiencies of 37%, exceeding the Shockley-Quiesser efficiency limit of 31% for photovoltaic conversion under unconcentrated sunlight. This represents a 250% increase in efficiency and 94% decrease in selective emitter area compared to a standard, angular-insensitive selective absorber.PACS: 42.70.Qs; 81.05.Xj; 78.67.Pt; 42.79.Ek.