The Arctic near-surface warming is much faster than its global counterpart. Yet, this Arctic amplification occurs a rate that is season, model and forcing-dependent. The present study aims at using temperature observations and reanalyses to constrain the projections of Arctic climate during the November-to-March season. Results show that the recently observed four-fold warming ratio is not entirely due to a human influence, and will decrease with increasing radiative forcings. Global versus regional temperature observations lead to complementary constraints on the projections. When Arctic amplification is defined as the additional polar warming relative to global warming, model uncertainties are narrowed by more than 30% after constraint. Similar results are obtained for projected changes in the Arctic sea ice extent (40%) and when using sea ice observations to constrain the polar warming (37%), thereby confirming the key role of sea ice as a positive but model, season and time-dependent surface feedback.