The combination of the Pine Island Ice Shelf (PIIS) draft and a seabed ridge beneath it form a topographic barrier, restricting access of warm Circumpolar Deep Water to a cavity inshore of the ridge, thus exerting an important control on PIIS basal ablation. In addition, PIIS has recently experienced several large calving events and further calving could significantly alter the cavity geometry. Changes in the ice front location, together with changes in ice thickness, might relax the topographic barrier and thus significantly change basal melt rates. Here, we consider the impact of past, and possible future, calving events on PIIS melt rates. We use a high‐resolution ocean model to simulate melt rates in both an idealized domain whose geometry captures the salient features of Pine Island Glacier, and a realistic geometry accurately resembling it, to explore how calving affects melt rates. The idealized simulations reveal that the melt response to calving has a sensitive dependence on the thickness of the gap between PIIS and the seabed ridge and inform our interpretation of the realistic simulations, which suggest that PIIS melt rates did not respond significantly to recent calving. However, the mean melt rate increases approximately linearly with further calving, and is amplified by approximately 10% relative to present day once the ice front reaches the ridge‐crest, taking less than one decade if calving maintains its present rate. This provides strong evidence that calving may represent an important, but as yet unexplored, contribution to the ice‐ocean sensitivity of the West Antarctic Ice Sheet.