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We perform a systematic survey of Titan's sharp‐edged depressions (SEDs) using a combination of Cassini synthetic aperture radar images and delay‐Doppler processed altimetry. We identify a characteristic bright‐dark pattern around 172 SEDs that correlates with elevated features only resolved with the highest resolution topographic data. We find that ∼75% of Titan's SEDs have elevated (∼100 m) rim features, with a preference toward larger SEDs. The differences in the distribution of SED rim presence between the north and south are slight, but the data weakly suggest that northern SEDs may be more likely to have a rim. The pattern we identify in synthetic aperture radar images is similar to quasi‐specular increases in backscatter seen on Titan's dunes. We show that this bright‐dark pattern occurs due to elevated local slopes oriented perpendicular to the radar. In general, rims occur on most of Titan's SEDs, an observation that will aid in developing and testing SED formation models. Plain Language Summary: Though they contain <1% of Titan's current liquids, Titan's sharp‐edged depressions (SEDs) are important geologic features whose formation and evolution may trace that of the polar regions as a whole. Distributed across both polar regions, these SEDs appear as closed depressions, in both a liquid‐filled and empty state. Our study uses high‐resolution topographic data and synthetic aperture radar image data to identify 100‐m‐high raised rims around most (75%) of these features. The origin of these features is not immediately clear. While the favored model for the formation of SEDs is dissolution erosion, dissolution is incompatible with the presence of these elevated rims. Our observations, though they add complications to current formation models, add an additional piece of information for future models to use as they continue to develop. Key Points: Raised rims are observable in SAR images and correlate with topographic highsMost sharp‐edged depressions (75%) have 100‐m raised rimsRim presence appears to depend on sharp‐edged depression size [ABSTRACT FROM AUTHOR]