We examine the long-period near-source ground motions from simulations of M 7.4 events on a strike-slip fault using kinematic ruptures with rupture speeds that range from subshear speeds through intersonic speeds to supersonic speeds. The strong along-strike shear-wave directivity present in scenarios with subshear rupture speeds disappears in the scenarios with ruptures propagating faster than the shear-wave speed. Furthermore, the maximum horizontal displacements and velocities rotate from generally fault-perpendicular orientations at subshear rupture speeds to generally fault-parallel orientations at supersonic rupture speeds. For rupture speeds just above the shear-wave speed, the orientations are spatially heterogeneous as a result of the random nature of our assumed slip model. At locations within a few kilometers of the rupture, the time histories of the polarization of the horizontal motion provide a better diagnostic with which to gauge the rupture speed than the orientation of the peak motion. Subshear ruptures are associated with significant fault-perpendicular motion before fault-parallel motion close to the fault; supershear ruptures are associated with fault-perpendicular motion after significant fault-parallel motion. Consistent with previous studies, we do not find evidence for prolonged supershear rupture in the long-period (>2 sec) ground motions from the 1979 Imperial Valley earthquake. However, we are unable to resolve the issue of whether a limited portion of the rupture (approximately 10 km in length) propagated faster than the shear-wave speed. Additionally, a recording from the 2002 Denali fault earthquake does appear to be qualitatively consistent with locally supershear rupture. Stronger evidence for supershear rupture in earthquakes may require very dense station coverage in order to capture these potentially distinguishing traits.