Antarctica's ice shelves play a key role in stabilizing the ice streams that feed them. Since basal melting largely depends on ice-ocean interactions, it is vital to attain consistent bathymetry models to estimate water and heat exchange beneath ice shelves. We have constructed bathymetry models beneath the ice shelves of western Dronning Maud Land by inverting airborne gravity data and incorporating seismic, multibeam, and radar depth references. Our models reveal deep glacial troughs beneath the ice shelves and terminal moraines close to the continental shelf breaks, which currently limit the entry of Warm Deep Water from the Southern Ocean. The ice shelves buttress a catchment that comprises an ice volume equivalent to nearly 1 m of eustatic sea level rise, partly susceptible to ocean forcing. Changes in water temperature and thermocline depth may accelerate marine-based ice sheet drainage and constitute an underestimated contribution to future global sea level rise.