The preservation and analysis of tombstones is important for historical, cultural, and artistic research. However, manually extracting information from photographs of these tombstones is laborious, which makes the use of automatic analysis methods desirable. We consider three types of tasks: text detection, text recognition, and end-to-end detection-recognition. For each of these tasks, we select two popular methods and evaluate their performance on two tombstone datasets. We use a dataset of German tombstones, featuring a wide variety of styles, and another dataset consisting of Dutch tombstones with more uniform designs. Prior to evaluation, we fine-tune each model on the training subset of the corresponding dataset. The results show that current methods can handle simple datasets such as the Dutch one, achieving detection and recognition error rates below 5%. In contrast, more complex data still pose as challenging, requiring improvements in model architecture, pre-training, or additional fine-tuning data. Furthermore, the performance of end-to-end systems can be considered as insufficient, with character recognition error rates around 20% even in the best-case scenarios. As such, while they offer acceptable results on some of the easiest data, current methods are not yet mature enough for reliable automated text extraction from these types of images.