We coupled together high-resolution versions of the ocean–sea ice model NEMO and the ice sheet model BISICLES configured to the Totten Glacier area and ran a series of simulations over the recent past (1995–2014) and under warming conditions (2081–2100; SSP4-4.5) with NEMO in stand-alone mode and with the coupled model to assess the effects of the coupling. During the recent past, the ocean–ice sheet coupling has increased the time-averaged value of the basal melt rate in both the Totten and Moscow University ice shelf cavities by 6.7% and 14.2%, respectively. The relationship between the changes in ice shelf thickness and ice shelf basal melt rate suggests that the effect of the coupling is not a linear response to the melt rate but rather a more complex response, driven partly by the dynamical component of the ice sheet model. The response of the ice sheet–ocean coupling due to the ocean warming is a 10% and 3% basal melt rate decrease in the Totten and Moscow University ice shelf cavities, respectively. This indicates that the ocean–ice sheet coupling under climate warming conditions dampens the basal melt rates. Our study highlights the importance of incorporating ocean–ice sheet coupling in climate simulations, even over short time periods.