The Energy Exascale Earth System Model (E3SM) is one of the few Earth system models that has the ability to simulate the ocean circulation in cavities beneath Antarctic ice shelves and its influence on ice-shelf basal melting, which is a critical control on ice shelf health, and hence ice discharge from the Antarctic Ice Sheet. Accurate representation of this circulation, the resulting water transformation and melt rate patterns are key for representing local, regional, and global feedbacks between the climate and sub-ice-shelf melting. Here, we investigate these processes in two different settings. First, we implement subglacial meltwater runoff as a grounding-line freshwater flux into the ocean and study its effect on ice-shelf basal melt rates and the polar climate under different runoff scenarios. Second, we investigate mesoscale heat transport into ice-shelf cavities and its impact on melting in a sequence of global, regionally refined configurations with nominal resolutions of 12, 8, 4, 2, and 1 km in the southern Weddell Sea. The analysis is focused on the Filchner-Ronne Ice Shelf, an important region for  projections of the contribution to sea-level change from the Antarctic Ice Sheet and for which there are relatively abundant observational datasets available for model validation.  These model developments and configurations are an important step towards full coupling between the Antarctic Ice Sheet and the climate system in E3SM.