Surface crevasses on the Greenland Ice Sheet capture nearly half of the seasonal runoff, yet their role in transferring meltwater to the bed has received little attention compared to that of supraglacial lakes and moulins. Here, we present observations of crevasse ponding and investigate controls on their hydrological behaviour at a fast-moving, marine-terminating sector of the Greenland Ice Sheet. We map surface meltwater, crevasses, and surface-parallel stress across a ~2,700 km² region using satellite data and contemporaneous uncrewed aerial vehicle (UAV) surveys. From 2017-2019 an average of 26% of the crevassed area exhibited ponding at locations that remained persistent between years despite rapid advection rates. We find that the spatial distribution of ponded crevasses does not relate to previously proposed methods for predicting the distribution of supraglacial lakes (elevation and topography) or crevasses (von Mises stress thresholds), suggesting the operation of some other physical control(s). Ponded crevasse fields were preferentially located in regions of compressive surface-parallel mean stress, which we interpret to result from the hydraulic isolation of these systems, in contrast to unponded crevasse fields, which we suggest are able to drain into the wider supraglacial and englacial network. UAV observations show that ponded crevasses can drain episodically and rapidly, likely through hydrofracture. We therefore propose that the surface stress regime informs a spatially heterogeneous transfer of meltwater through crevasses to the bed of ice sheets, with potential consequences for processes such as subglacial drainage and the heating of ice via latent heat release by refreezing meltwater.