Predicting streamflow hydrographs in ungauged catchments is challenging, and accompanying the estimates with realistic uncertainty bounds is an even more complex task. In this paper, we present a method to transfer global uncertainty estimates from gauged to ungauged catchments and we test it over a set of 907 catchments located in France, using two rainfall–runoff models. We evaluate the quality of the uncertainty estimates based on three expected qualities: reliability, sharpness, and overall skill. The robustness of the method to the availability of information on gauged catchments was also evaluated using a hydrometrical desert approach. Our results show that the method presents advantageous perspectives, providing reliable and sharp uncertainty bounds at ungauged locations in a majority of cases.