This letter presents a new cavity-based approach for measuring the radiation efficiency of ultrawideband (UWB) antennas. The procedure is based on a generalized Wheeler cap method that is only practical for narrowband measurements, and so this letter introduces an extension to UWB using source-stirring. The number of required measurements needed is relatively low and independent of the frequency span, therefore making the technique convenient for UWB. A complete post-processing procedure to automatically identify and remove erroneous radiation efficiency predictions is presented. The new method was tested with a coplanar-fed UWB monopole and compared to existing UWB efficiency cavity-based measurement methods. The results show good agreement with simulations and compare favorably to other UWB-centric methods, confirming the proposed approach as a good alternative to measure UWB antenna radiation efficiency.