Protected areas may be important refuges for large carnivores, but many are not large enough to sustain viable populations. Without sufficient dispersal between protected areas, large carnivore populations inside them are at risk of becoming genetically isolated and demographically vulnerable. In this study, we use the jaguar population in and around Emas National Park in the Brazilian Cerrado as a case study to evaluate the demographic sustainability of a large carnivore population within a small and potentially isolated protected area. We used camera trapping data and spatially explicit capture-recapture models to estimate density and corresponding population size of jaguars in Emas National Park. We then used a matrix-based age and sex structured stochastic population model to evaluate the demographic viability of jaguar populations across a range of population sizes, including those estimated for Emas. We detected 10 individual jaguars during our survey with a total of 74 detections. Our density estimation became unbiased using a buffer width of 30 km and produced a density of 0.17 jaguars per 100 km(2). The estimated population sizes of 10-60 animals suffered extinction risks of 70-90% without net immigration. However, only a low number of immigrants were required to suppress extinction risk towards zero. Our density estimate for jaguars was lower than in previous studies, and our simulations suggested that this population may have a substantial extinction risk. Ensuring dispersal and connectivity outside of protected areas, through the implementation of habitat corridors, can greatly reduce this extinction risk, and we suggest that this scenario is potentially applicable to many other large carnivore populations.