Places of past conflicts and persistent objects that reflect such events often attract the attention of archaeological prospection which facilitates the construction of conflict narratives. Field prospection as a precise method for localization of aerial bombing craters (as an example of such persistent features) is a highly time- and resource-consuming task. Therefore, methods for automatic identification of such features are evolving. We present a comparison of three methods for possible automatic crater detection based on (a) extraterrestrial crater detection algorithms, (b) geomorphology-based edge extraction, and (c) image pattern recognition via a state-of-the-art convolutional neural network (CNN). All methods were preliminarily tested on a case study of eight Second World War (WWII) aerial bombing crater sites in NW Czechia via Airborne Laser Scanned LiDAR-derived digital terrain models with different spatial resolutions. We found that extraterrestrial crater detection algorithms and geomorphology-based edge extraction methods yield worse results given the standard indices of precision and recall. By comparison, the CNN method utilized for a particular task achieved satisfying results, predominantly with 0.5 m/px resolution (which is often available at the country level) of the input raster. Nevertheless, overall performance with this resolution varies significantly among the sites. Therefore, the quality and readability of the input data are crucial factors for the successful acquisition of precise ordinance location identification.