The tomb compound adjoining the Grand Mosque holds the bones of Panembahan Senopati, founder of the second Mataram Sultanate around 1587, along with his closest family and several later princes. It is a working pilgrimage site rather than a tourist attraction — Javanese visitors come to meditate, present petitions and bring offerings — and you should treat it accordingly.
The main tomb chamber is open to the public only on certain days (typically Mondays, Thursdays and Fridays). To enter you must change into Javanese court dress: a sarong, kebaya for women, surjan jacket and blangkon headcloth for men, all of which are rented for a few thousand rupiah at the gate. Photography inside the tomb is forbidden. The outer courtyard, with its ancient banyans and the sacred Sendang Seliran spring used for ritual bathing, can be visited any time.