The processes responsible for freshwater flux from the Antarctic Ice Sheet (AIS), ice‐shelf basal melting and iceberg calving, are generally poorly represented in current Earth System Models (ESMs). Here we document the cryosphere configuration of the U.S. Department of Energy's Energy Exascale Earth System Model (E3SM) v1.2. This includes simulating Antarctic ice‐shelf basal melting, which has been implemented through simulating the ocean circulation within static Antarctic ice‐shelf cavities, allowing for the ability to calculate ice‐shelf basal melt rates from the associated heat and freshwater fluxes. In addition, we added the capability to prescribe forcing from iceberg melt, allowing for realistic representation of the other dominant mass loss process from the AIS. In standard resolution simulations (using a noneddying ocean) under preindustrial climate forcing, we find high sensitivity of modeled ocean/ice shelf interactions to the ocean state, which can result in a transition to a high basal melt regime under the Filchner‐Ronne Ice Shelf (FRIS), presenting a significant challenge to representing the ocean/ice shelf system in a coupled ESM. We show that inclusion of a spatially dependent parameterization of eddy‐induced transport reduces biases in water mass properties on the Antarctic continental shelf. With these improvements, E3SM produces realistic ice‐shelf basal melt rates across the continent that are generally within the range inferred from observations. The accurate representation of ice‐shelf basal melting within a coupled ESM is an important step toward reducing uncertainties in projections of the Antarctic response to climate change and Antarctica's contribution to global sea‐level rise. Plain Language Summary The future of the Antarctic Ice Sheet (AIS) has the potential to have broad impacts on global climate, perhaps most notably in contributing to sea‐level rise. The current generation of Earth System Models (ESMs) do not accurately represent the two primary means in which ice is lost from the AIS, through melting at the base of ice shelves floating on the ocean and the calving of icebergs. This limits our ability to make climate projections that incorporate the impacts of the AIS in a changing climate. Here, we demonstrate a novel capability to model one of those processes, ice‐shelf basal melting, in an ESM. We demonstrate the ability to simulate ice‐shelf basal melt rates across many Antarctic ice shelves that are in line with present day observations. We also find that, for certain ice shelves, modeled ice‐shelf basal melting can experience a rapid transition to high melting far above present‐day estimates, and this simulated high melting can be mitigated through improved ocean physics. Key Points Capabilities have been added to an Earth System Model to model realistic Antarctic ice‐shelf basal melt fluxes and prescribe iceberg forcing Simulated basal melt rates have a strong sensitivity to the ocean mesoscale eddy parameterization For one choice of the mesoscale eddy parameterization, the Filchner‐Ronne Ice Shelf transitions to a high melt regime