Subglacial hydrologic systems in Antarctica and Greenland play a fundamental role in ice-sheet dynamics, yet critical aspects of these systems remain poorly understood due to a lack of observations. Ground-based electromagnetic (EM) geophysical methods are established for mapping groundwater in many environments, but have never been applied to imaging lakes beneath ice sheets. Here, we study the feasibility of passive- and active-source EM imaging for quantifying the nature of subglacial water systems beneath ice streams, with an emphasis on the interfaces between ice and basal meltwater, as well as deeper groundwater in the underlying sediments. We describe a suite of model studies that exam the data sensitivity as a function of ice thickness, water conductivity and hydrologic system geometry for models representative of a subglacial lake and a grounding zone estuary. We show that EM data are directly sensitive to groundwater and can image its lateral and depth extent. By combining the conductivity obtained from EM data with ice thickness and geological structure from conventional geophysical techniques, such as ground-penetrating radar and active seismic surveying, EM data have the potential to provide new insights on the interaction between ice, rock and water at critical ice-sheet boundaries.