Following rapid atmospheric warming over the past decades2, 3, Antarctic Peninsula ice shelves have progressively retreated4, at times catastrophically5. This decay supports hypotheses of thermal limits of viability for ice shelves via surface melt forcing3, 5, 6. Here we use a polar-adapted regional climate model7 and satellite observations8 to quantify the nonlinear relationship between surface melting and summer air temperature. Combining observations and multimodel simulations, we examine melt evolution and intensification before observed ice shelf collapse on the Antarctic Peninsula. We then assess the twenty-first-century evolution of surface melt across Antarctica under intermediate and high emissions climate scenarios. Our projections reveal a scenario-independent doubling of Antarctic-wide melt by 2050. Between 2050 and 2100, however, significant divergence in melt occurs between the two climate scenarios. Under the high emissions pathway by 2100, melt on several ice shelves approaches or surpasses intensities that have historically been associated with ice shelf collapse, at least on the northeast Antarctic Peninsula.