We present the first results of a Near-UltraViolet (NUV) survey of RR Lyrae stars from the Ultraviolet Optical Telescope (UVOT) on board the Swift Gamma-ray Burst Mission. It is well-established that RR Lyrae stars have large amplitudes in the far- and near-ultraviolet. We have used UVOT's unique wide-field NUV imaging capability to perform the first systematic NUV survey of variable stars in the Galactic globular clusters M3 and M15. We identify 280 variable stars, comprised of 275 RR Lyrae, 2 anomalous Cepheids, 1 classical Cepheid, 1 SX Phoenicis star, and 1 possible long-period or irregular variable. Only two of these are new discoveries. We compare our results to previous investigations and find excellent agreement in the periods with significantly larger amplitudes in the NUV. We map out, for the first time, an NUV Bailey diagram from globular clusters, showing the usual loci for fundamental mode RRab and first overtone RRc pulsators. We show the unique sensitivity of NUV photometry to both the temperatures and the surface gravities of RR Lyrae stars. Finally, we show evidence of an NUV period-metallicity-luminosity relationship. Future investigations will further examine the dependence of NUV pulsation parameters on metallicity and Oosterhoff classification.