Despite multiple advances in the understanding of the water cycle intensification in a warmer climate, climate models still diverge in their hydrological projections. Here we constrain annual runoff projections over individual and aggregated Arctic river basins. For this purpose, we use two ensembles of global climate models and two statistical methods: a regression scheme assuming similar runoff sensitivities at interannual versus climate change timescales, and a Bayesian method where models are used to derive a posterior runoff response conditional to historical observations. While both techniques are shown to narrow model uncertainties, more or less substantially depending on rivers, the Bayesian method is less sensitive to the choice of the model ensemble and is more skilful when tested with synthetic observations. It has also been applied over the whole Arctic watershed, showing so far a limited narrowing of the inter-model spread, but its skill will further improve with increasing climate change.