Sea level rise is expected to be rapid and extremely damaging to coastal communities and infrastructure, with unavoidable losses and coastal protection costs in the tens of billions per year. Retreat of the Thwaites and Pine Island Glaciers is likely already in an unstable regime as their oceanic fronts are ablated by deep intruding layers of relatively warm seawater. Warm water can be blocked from reaching the grounding line by thin flexible buoyant curtains anchored to the seabed. The consequent reduction in ice shelf melting could result in increased ice sheet buttressing as the shelf makes contact with seabed highs. Flexible curtains are less costly than solid artificial barriers, more robust against iceberg collisions, and easier to repair or remove in the event of unforeseen side effects. We illustrate the technical viability of this approach by considering curtain design concepts that should withstand oceanographic forces, and feasible methods of installation. Suitable materials are commonly available. Installation of a seabed curtain in temperate ocean waters would be entirely within the capabilities of existing offshore and deep ocean construction techniques. Installing in polar waters presents severe challenges from icebergs, harsh weather, and brief working seasons, which can however, be overcome with present-day technology. An 80 km long curtain installed in 600 m deep waters on alluvial sediments could help stabilize Pine Island and Thwaites glaciers over the next few centuries at much lower cost ($40-80 billion + $1-2 billion/yr maintenance) than the global coastline protection (∼$40 billion/yr) needed due to their collapse.