Limburg Castle (Schloss Limburg) sits on the same rocky outcrop as the cathedral, just to the east of the Dom. The complex grew from a tenth-century fortified residence into a late-medieval palace and has been remodelled repeatedly; the oldest surviving sections are the thirteenth-century keep and great hall.
Today the castle houses the city museum (Stadtmuseum), which traces Limburg's history from its founding through the medieval cloth and trade boom to the modern day. Even if you skip the interior, the castle terrace is worth the climb for the view across the Lahn valley.