Simulations of ice-shelf basal melting in future climate scenarios from the IPCC’s Fourth Assessment Report (AR4) have revealed a large uncertainty and the potential of a rapidly increasing basal mass loss particularly for the large cold-water ice shelves in the Ross and Weddell Seas. The large spread in model results was traced back to uncertainties in the freshwater budget on the continental shelf, which is governed by sea-ice formation. Differences in sea-ice formation, in turn, were shown to follow the regional differences between the atmospheric heat fluxes imprinted by the climate models. A more recent suite of FESOM model experiments was performed with output from two members of the newer generation of climate models engaged in the IPCC’s Fifth Assessment Report (AR5). Comparing simulations forced with output from the AR5/CMIP5 models HadGem2 and MPI-ESM, we find that projected heat fluxes and thus sea-ice formation over the Southern Ocean continental shelves have converged to an ensemble with a much smaller spread than between the AR4 experiments. For most of the modeled ice shelves, a gradual but accelerating increase of basal melt rates during the 21st century is a robust feature. Both with HadGem2 and with MPI-ESM forcing, basal melt rates for the Filchner–Ronne Ice Shelf in FESOM increase by a factor of two by the end of the 21st century in the RCP85 scenario. For the smaller, warm-water ice shelves, inter-model differences in ice-shelf basal mass loss projections are still slightly larger than differences between the scenarios RCP45 and RCP85; compared with AR4 projections, however, the model-dependent spread has been strongly reduced. Current work aims at further reducing the uncertainties arising from atmospheric forcing by using output from the regional climate model RACMO. The effect of a varying cavity geometry and the response of the grounded ice are being adressed by coupling to the RIMBay ice shelf / ice sheet model.