The shape and extent of the Greenland Ice Sheet (GIS) during the Last Interglacial (LIG) is a matter of controversy, with different studies proposing a wide range of reconstructions. Here, for the first time, we combine stable water isotopic information from ice cores with isotope‐enabled climate model outputs to investigate the problem. Exploring the space of possible ice sheet geometries by simulation is prohibitively expensive. We address this problem by using a Gaussian process emulator as a statistical surrogate of the full climate model. The emulator is calibrated using the results of a small number of carefully chosen simulations and then permits fast, probabilistic predictions of the simulator outputs at untried inputs. The inputs are GIS morphologies, parameterized through a dimension‐reduction technique adapted to the spherical geometry of the setting. Based on the emulator predictions, the characteristics of morphologies compatible with the available ice core measurements are explored, leading to a reduction in uncertainty on the LIG GIS morphology. Moreover, a scenario‐based approach allows to assess the gains in uncertainty reduction which would result from the availability of better dated LIG measurements in Greenland ice cores.