A method for accurate estimation of surface-wave magnitudes is presented as an alternative to Ms, the classical time-domain magnitude. The salient features of the method are the use of velocity and frequency windows to isolate seismic phases and the use of maximum spectral energy to characterize ground motion for magnitude estimation. Rayleigh-wave ground motion estimated by the new method is generally consistent, but not identical, to that measured in the time domain. The estimated ground motion is used to determine Rayleigh-wave spectral magnitudes for 27 presumed nuclear explosions, from several test sites. These magnitudes are studied for their accuracy and for their transportability between nuclear explosion test sites. For accuracy, we compare spectral magnitudes MR with their corresponding time-domain-measured magnitudes Ms. The comparison encompasses network magnitudes and their standard deviations and magnitude residuals. For transportability, we studied the variations in mb (body-wave magnitude), Ms (time-domain magnitude), and MR (spectral magnitude) for network-averaged mb-equivalent presumed nuclear explosions at the Shagan River and the Qingger test sites. These studies showed that this spectral magnitude has a smaller error than classical time-domain Ms and that it is transportable between the two test sites.