Changes in basal melting of ice shelves is expected to be the largest control on future mass change and the associated sea level contribution from the Antarctic Ice Sheet, yet ice shelf melt fluxes have been absent from Earth system models until very recently. Using different configurations of the ocean component in the Department of Energy’s Energy Exascale Earth System Model (E3SM), we explore what key processes are required for realistic representation of ice-shelf basal melting. We find that the representation of mesoscale eddy transport at low resolution is a critical control on continental shelf water properties, which in turn determine ice-shelf basal melt rates. Modest biases in ocean temperature and salinity can trigger tipping points between stable ocean states that result in order of magnitude changes in modeled ice-shelf basal melt rates, resulting in unrealistic simulations of the Antarctic and, in turn, the global climate system. This sensitivity of ocean/ice shelf interactions to ocean stratification creates a significant challenge in representing the coupled ocean/ice shelf system in Earth system models. We show that inclusion of a spatially-dependent parameterization of eddy-induced transport at low resolution reduces model biases in water mass properties on the Antarctic continental shelf and the strength of the Antarctic Slope Front. With these improvements, E3SM produces realistic and stable ice-shelf basal melt rates across the continent under preindustrial and historical climate forcing. This configuration provides a platform for assessing the stability of marine sectors of the Antarctic Ice Sheet under future climate scenarios and the global climatic impacts of changes in ice-shelf melting.