Unmanned aerial systems (UASs) are widely used for remote sensing, including the production of high-resolution digital elevation models (DEMs). We study the possibilities of UAS-based aerial surveys to produce photogrammetrically sound, high-resolution DEMs intended for geomorphometric modeling. The study was conducted at the Zaoksky testing ground (Russia). To carry out an aerial survey, we used a UAS Geoscan-101 equipped with a Sony DSC-RX1 camera and a Topcon GNSS receiver. Aerial photographs were processed using Agisoft PhotoScan Professional software. Applying dense point cloud generation and classification, we produced DEMs with resolutions of 6 cm, 20 cm, and 1 m. Using a universal spectral analytical method, we derived models of several morphometric variables (i.e., slope gradient, horizontal, vertical, minimal, and maximal curvatures) from DEMs with resolutions of 20 cm and 1 m. We found that it is possible to produce noiseless models and well-readable maps of morphometric variables for grassy areas with separately standing groups of trees and shrubs. However, UAS-based DEMs cannot be applied for modeling of forested areas: there occur pronounced unrecoverable artifacts due to errors of automated classification of the dense point cloud. Finally, we present recommendations for the production of UAS-derived, photogrammetrically sound, high-resolution DEMs intended for geomorphometry.