In Northern Europe, parish records provide centuries of lineage information, useful not only for settling inheritance disputes, but also for studying hereditary diseases, social mobility, etc. The key information to extract from scans of parish records to obtain lineage information is dates: birth dates (of children and their parents) and dates of baptisms. We present a new dataset of birth dates from Danish parish records and use it to benchmark different approaches to handwritten date recognition, some based on classification and some based on transduction. We evaluate these approaches across several experimental protocols and different segmentation strategies. A state-of-the-art transformer-based transduction model exhibits lower error rates than image classifiers in most scenarios. The image classifiers can nevertheless offer a compelling trade-off in terms of accuracy and computational resource requirements.