Species that are distributed over wide geographical ranges are likely to encounter a greater diversity of environmental conditions than do narrowly distributed taxa, and thus we expect a correlation between size of geographical range and breadth of physiological tolerances to abiotic challenges. That correlation could arise either because higher physiological capacity enables range expansion, or because widely distributed taxa experience more intense (but spatially variable) selection on physiological tolerances. The invasion of oceanic habitats by amniotic vertebrates provides an ideal system with which to test the predicted correlation between range size and physiological tolerances, because all three lineages that have secondarily moved into marine habitats (mammals, birds, reptiles) exhibit morphological and physiological adaptations to excrete excess salt. Our analyses of data on 62 species (19 mammals, 18 birds, 24 reptiles) confirm that more-widely distributed taxa encounter habitats with a wider range of salinities, and that they have higher osmoregulatory ability as determined by sodium concentrations in fluids expelled from salt-excreting organs. This result remains highly significant even in models that incorporate additional explanatory variables such as metabolic mode, body size and dietary habits. Physiological data thus may help to predict potential range size and perhaps a species’ vulnerability to anthropogenic disturbance.