Surface melting occurs during summer on the Antarctic and Greenland ice sheets, but the volume of stored surface meltwater has been difficult to quantify due to a lack of accurate depth estimates. NASA's ICESat-2 laser altimeter brings a new capability: photons penetrate water and are reflected from both the water and the underlying ice; the difference provides a depth estimate. ICESat-2 sampled Amery Ice Shelf on January 2, 2019 and showed double returns from surface depressions, indicating meltwater. For four melt features, we compared depth estimates from eight algorithms: six based on ICESat-2 and two from coincident Landsat-8 and Sentinel-2 imagery. All algorithms successfully identified surface water at the same locations. Algorithms based on ICESat-2 produced the most accurate depths; the image-based algorithms underestimated depths (by 30%–70%). This implies that ICESat-2 depths can be used to tune image-based algorithms, moving us closer to quantifying stored meltwater volumes across Antarctica and Greenland.