Climate change is having profound effects on the distributions of species globally. Trait-based assessments predict that specialist and range-restricted species are among those most likely to be at risk of extinction from such changes. Understanding individual species' responses to climate change is therefore critical for informing conservation planning. We use an established Species Distribution Modelling (SDM) protocol to describe the curious range-restriction of the globally threatened White-tailed Swallow (Hirundo megaensis) to a small area in southern Ethiopia. We find that, across a range of modelling approaches, the distribution of this species is well described by two climatic variables, maximum temperature and dry season precipitation. These same two variables have been previously found to limit the distribution of the unrelated but closely sympatric Ethiopian Bush-crow (Zavattariornis stresemanni). We project the future climatic suitability for both species under a range of climate scenarios and modelling approaches. Both species are at severe risk of extinction within the next half century, as the climate in 68-84% (for the swallow) and 90-100% (for the bush-crow) of their current ranges is predicted to become unsuitable. Intensive conservation measures, such as assisted migration and captive-breeding, may be the only options available to safeguard these two species. Their projected disappearance in the wild offers an opportunity to test the reliability of SDMs for predicting the fate of wild species. Monitoring future changes in the distribution and abundance of the bush-crow is particularly tractable because its nests are conspicuous and visible over large distances.