Warm water masses circulating at depth off the coast of Greenland play an important role in controlling rates of mass loss from the Greenland Ice Sheet through feedbacks associated with the melting of marine glacier termini. The ability of these warm waters to reach glacier termini is strongly controlled by fjord bathymetry, which was unmapped for the majority of Greenland's fjords until recently. In response to the need for bathymetric measurements in previously uncharted areas, we developed two companion methods to infer fjord bathymetry using icebergs as depth sounders. The main premise of our methods centers around the idea that deep-drafted icebergs will become stranded in shallow water such that estimates of iceberg surface elevation can be used to infer draft, and thus water depth, under the assumption of hydrostatic equilibrium. When and where available, surface elevations of icebergs stranded on bathymetric highs were extracted from digital elevation models (DEMs) and converted to estimates of iceberg draft. To expand the spatial coverage of our inferred water depths beyond the DEM footprints, we used the DEMs to construct characteristic depth-width ratios and then inferred depths from satellite imagery-derived iceberg widths. We tested and applied the methods in two fjord systems in western Greenland with partially constrained bathymetry, Ilulissat Isfjord and Naajarsuit Fjord, to demonstrate their utility for inferring bathymetry using remote sensing datasets. Our results show that while the uncertainties associated with the methods are high (up to ±93 m), they provide critical first-order constraints on fjord bathymetry.