Predicting whether the ranges of tropical species will shift to higher elevations in response to climate change requires models that incorporate data on topography and land use. We incorporated temperature gradients and land-cover data from the current ranges of species in a model of range shifts in response to climate change. We tested four possible scenarios of amphibian movement on a tropical mountain: movement upslope through and to land cover suitable for the species; movement upslope to land-cover types that will not sustain survival and reproduction; movement upslope to areas that previously were outside the species’ range; and movement upslope to cooler areas within the current range. Areas in the final scenario will become isolated as climate continues to change. In our scenarios more than 30% of the range of 21 of 46 amphibian species in the tropical Sierra Nevada de Santa Marta is likely to become isolated as climate changes. More than 30% of the range of 13 amphibian species would shift to areas that currently are unlikely to sustain survival and reproduction. Combined, over 70% of the current range of seven species would become thermally isolated or shift to areas that currently are unlikely to support survival and reproduction. The constraints on species’ movements to higher elevations in response to climate change can increase considerably the number of species threatened by climate change in tropical mountains.