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Abstract Morphological processes often induce meter‐scale elevation changes. When a volcano erupts, tracking such processes provides insights into the style and evolution of eruptive activity and related hazards. Compared to optical remote‐sensing products, synthetic aperture radar (SAR) observes surface change during inclement weather and at night. Differential SAR interferometry estimates phase change between SAR acquisitions and is commonly applied to quantify deformation. However, large deformation or other coherence loss can limit its use. We develop a new approach applicable when repeated digital elevation models (DEMs) cannot be otherwise retrieved. Assuming an isotropic radar cross‐section, we estimate meter‐scale vertical morphological change directly from SAR amplitude images via an optimization method that utilizes a high‐quality DEM. We verify our implementation through simulation of a collapse feature that we modulate onto topography. We simulate radar effects and recover the simulated collapse. To validate our method, we estimate elevation changes from TerraSAR‐X stripmap images for the 2011–2012 eruption of Mount Cleveland. Our results reproduce those from two previous studies; one that used the same dataset, and another based on thermal satellite data. By applying this method to the 2019–2020 eruption of Shishaldin Volcano, Alaska, we generate elevation change time series from dozens of co‐registered TerraSAR‐X high‐resolution spotlight images. Our results quantify previously unresolved cone growth in November 2019, collapses associated with explosions in December–January, and further changes in crater elevations into spring 2020. This method can be used to track meter‐scale morphology changes for ongoing eruptions with low latency as SAR imagery becomes available.