Relative sea level (local water depth) on the Antarctic continental shelf is changing by the complex interplay of processes associated with Glacial Isostatic Adjustment (GIA). This involves near-field visco-elastic bedrock displacement and self-gravitational effects in response to changes in Antarctic ice load, but also far-field interhemispheric effects on the sea-level pattern. On glacial time scales, these changes can be in the order of several hundred meters, modulating the access of ocean water masses at different depths to Antarctic grounding lines. Our study shows, that due to strong vertical gradients in ocean temperature and salinity at the continental shelf margin, basal melt rates of ice shelves can change significantly just by variations in relative sea level alone. Based on coupled ice sheet – GIA model experiments and the analysis of topographic features such as troughs and sills that regulate the access of open ocean water masses onto the continental shelf (oceanic gateways), we derive maximum estimates of Antarctic basal melt rate changes, solely driven by relative sea-level variations. Under Last Glacial Maximum sea-level conditions, this effect would lead to a substantial decrease of present-day sub-shelf melt rates in East Antarctica, while the strong subsidence of bedrock in West Antarctica can lead up to a doubling of basal melt rates. For a hypothetical globally ice-free sea-level scenario, which would lead to a global mean (barystatic) sea-level rise of around +70 m, sub-shelf melt rates for a present-day ice sheet geometry can more than double in East Antarctica, but can also decrease substantially, where bedrock uplift dominates. Also for projected sea-level changes at the year 2300 we find maximum possible changes of ±20 % in sub-shelf melt rates, as a consequence of relative sea-level changes only.