Plant species have responded to recent increases in global temperatures by shifting their geographical ranges poleward and to higher altitudes. Bioclimate models project future range contractions of montane species as suitable climate space shifts uphill. The species–climate relationships underlying such models are calibrated using data at either ‘macro’ scales (coarse resolution, e.g. 50 km × 50 km, and large spatial extent) or ‘local’ scales (fine resolution, e.g. 50 m × 50 m, and small spatial extent), but the two approaches have not been compared. This study projected macro (European) and local models for vascular plants at a mountain range in Scotland, UK, under low (+1.7 °C) and high (+3.3 °C) climate change scenarios for the 2080s. Depending on scenario, the local models projected that seven or eight out of 10 focal montane species would lose all suitable climate space at the site. However, the European models projected such a loss for only one species. The cause of this divergence was investigated by cross-scale comparisons of estimated temperatures at montane species' warm range edges. The results indicate that European models overestimated species' thermal tolerances because the input coarse resolution climate data were biased against the cold, high-altitude habitats of montane plants. Although tests at other mountain ranges are required, these results indicate that recent large-scale modelling studies may have overestimated montane species' ability to cope with increasing temperatures, thereby underestimating the potential impacts of climate change. Furthermore, the results suggest that montane species persistence in microclimatic refugia might not be as widespread as previously speculated.