Climate modes as simulated by global climate models are often found to be considerably weaker than are observed. One possibility is that coarse‐resolution climate models do not capture turbulent air–sea fluxes sufficiently. Ensemble experiments with the same atmospheric configuration of the Met Office Hadley Centre climate model, forced with observed sea‐surface temperatures (SST) and at three different horizontal model resolutions (approximately 130, 60 and 25 km), are used to test the sensitivity of air–sea surface heat and moisture fluxes. We find that, although global mean budgets at the three resolutions are very similar, substantial differences appear in regional air–sea flux patterns. Increased model resolution consistently enhances zonal‐mean air–sea fluxes in the mid–high latitudes while suppressing heat fluxes in the low latitudes and weakening the Hadley Circulation. In the North Atlantic, annual mean surface heat fluxes into the atmosphere along the Gulf Stream/North Atlantic Current and over the sub‐polar gyre can increase by up to 10 W/m2 when atmospheric model resolution increases from 130 to 60 km. In the Pacific, increased model resolution tends to weaken the Walker Circulation with increased heat fluxes from the east but markedly reduced fluxes from the western Pacific, leading to significantly improved precipitation over the tropical western Pacific and the Maritime Continent. Changes in air–sea heat fluxes come about mainly as a result of changed near‐surface ventilation. Generally, increasing resolution strengthens surface winds and reduces specific humidity in the mid–high latitudes while weakening surface winds over the Tropics and subtropics.