State-of-the-art Earth system models, like the ones used in CMIP6, suffer from temporal inconsistencies at the ocean–atmosphere interface. In this study, a mathematically consistent iterative Schwarz method is used as a reference. Its tremendous computational cost makes it unusable for production runs, but it allows us to evaluate the error made when using legacy coupling schemes. The impact on the climate at longer timescales of days to decades is not evaluated.