Antarctic ice-shelf stability is threatened by surface melt, which has been implicated in several ice-shelf collapse events over recent decades. Here, we first analyze cumulative days of wet snow/ice status ("melt days") for melt seasons from 1980 to 2021 over Antarctica's ice shelves using passive and active microwave satellite observations. As these observations do not directly reveal meltwater volumes, we calculate these using the physics-based multi-layer snow model SNOWPACK, driven by the global climate-reanalysis model Modern-Era Retrospective analysis for Research and Applications Version 2. We find a strong non-linear relationship between melt days and meltwater production volume. SNOWPACK's calculation of melt days shows agreement with observations of both cumulative days, and spatial and interannual variability. Highest melt rates are found on the Peninsula ice shelves, particularly in the 1992/1993 and 1994/1995 austral summers. Over all ice shelves, SNOWPACK calculates a small, but significant, decreasing trend in both annual melt days and meltwater production volume over the 41 years.