We investigate the details of the trajectory of ions that are initially specularly reflected at a planar quasi-perpendicular (where the angle θBn between the upstream magnetic field and shock normal directions exceeds 45°) collisionless shock. In the first of two separate studies we examine the possibility of multiple reflections at the shock front. The number of times an ion re-encounters the shock increases as the shock geometry becomes more perpendicular. However, the length of time spent by the ion interacting with the shock, a parameter of relevance to the effectiveness of the particles acceleration by the shock, does not increase monotonically with θBn due to the details of the particles trajectory. The interaction time is also a strong function of the particles initial normal speed. In a second study, the trajectories of ions able to overcome the shock potential are followed downstream. For θBn ⩽ 60°, ions which cross the potential jump at their first re-encounter with the shock eventually escape upstream after two, four or six shock traversals, depending on the value of θBn. The particles interaction time with the shock rises rapidly with the number of re-encounters and generally, though not always, with θBn. The magnitude of the electrostatic potential and the Mach number of the upstream flow have a very minor effect on particle trajectories. For θBn > 60°, particles that cross the shock remain downstream unless they traverse the shock after having undergone further specular reflections. Multiple shock crossings can lead to a significant increase in the upstream extent of an ions trajectory relative to that reached after the initial specular reflection.