It is often unclear how to optimally choose horizontal resolution for the oceanic and atmospheric components of coupled climate models, which has implications for their ability to make best use of available computational resources. Here we investigate the effect of using different combinations of horizontal resolutions in atmosphere and ocean on the simulated climate in a global coupled climate model (Alfred Wegener Institute Climate Model [AWI-CM]). Particular attention is given to the Atlantic Meridional Overturning Circulation (AMOC). Four experiments with different combinations of relatively high and low resolutions in the ocean and atmosphere are conducted. We show that increases in atmospheric and oceanic resolution have clear impacts on the simulated AMOC, which are largely independent. Increased atmospheric resolution leads to a weaker AMOC. It also improves the simulated Gulf Stream separation; however, this is only the case if the ocean is locally eddy resolving and reacts to the improved atmosphere. We argue that our results can be explained by reduced mean winds caused by higher cyclone activity. Increased resolution of the ocean affects the AMOC in several ways, thereby locally increasing or reducing the AMOC. The finer topography (and reduced dissipation) in the vicinity of the Caribbean basin tends to locally increase the AMOC. However, there is a reduction in the AMOC around 45°N, which relates to the reduced mixed layer depth in the Labrador Sea in simulations with refined ocean and changes in the North Atlantic current pathway. Furthermore, the eddy-induced changes in the Southern Ocean increase the strength of the deep cell.