The archaeological museum occupies a vaulted hall in the lower courtyard of the castle. The display is modest but well chosen: Iron Age and Nabataean pottery from the surrounding hills, Crusader weaponry, Mamluk inscriptions, and several handsome carved capitals. The information panels (in English and Arabic) are particularly good on the political shifts that gave the castle each of its layers.
The museum is included in the castle ticket. Allow half an hour; it pairs naturally with a walk through the upper galleries above. If you are interested in the wider region, much of the headline material from Karak ends up in the Jordan Museum in Amman, but the local display gives a satisfying sense of place.