Ice shelf break-up and disintegration events over the past 5 decades have led to speed-up, thinning, and retreat of upstream tributary glaciers and increases to rates of global sea-level rise. The southward progression of these episodes indicates a climatic cause and in turn suggests that the larger Larsen C and George VI ice shelves may undergo a similar collapse in the future. However, the extent to which removal of the Larsen C and George VI ice shelves will affect upstream tributary glaciers and add to global sea levels is unknown. Here we apply numerical ice-sheet models of varying complexity to show that the centennial sea-level commitment of Larsen C embayment glaciers following immediate shelf collapse is low ( < 2.5 mm to 2100, < 4.2 mm to 2300). Despite its large size, Larsen C does not provide strong buttressing forces to upstream basins and its collapse does not result in large additional discharge from its tributary glaciers in any of our model scenarios. In contrast, the response of inland glaciers to a collapse of the George VI Ice Shelf may add up to 8 mm to global sea levels by 2100 and 22 mm by 2300 due in part to the mechanism of marine ice sheet instability. Our results demonstrate the varying and relative importance to sea level of the large Antarctic Peninsula ice shelves considered to present a risk of collapse.