We investigate the excitation and propagation of equatorial magnetosonic waves observed by the Van Allen Probes, and describe evidence for a trapping mechanism for magnetosonic waves in the Earth's plasmasphere. Intense equatorial magnetosonic waves were observed inside the plasmasphere in association with a pronounced proton ring distribution, which provides free energy for wave excitation. Instability analysis along the inbound orbit demonstrates that broad-band magnetosonic waves can be excited over a localized spatial region near the plasmapause. The waves can subsequently propagate into the inner plasmasphere and remain trapped over a limited radial extent, consistent with the predictions of near-perpendicular propagation. By performing a similar analysis on another observed magnetosonic wave event, we demonstrate that magnetosonic waves can also be trapped within local density structures. We suggest that perpendicular wave propagation is important for explaining the presence of magnetosonic waves in the Earth's plasmasphere at locations away from the generation region.