Moses married his cousin Catherine Mendes in 1698. Catherine had been baptized in Somerset House and was named after Catherine of Braganza, wife of King Charles II. Catherine da Costa made the water-colour portrait of her father which now hangs in the vestry of the Bevis Marks Synagogue. Their children included Sarah (Simha) Mendes da Costa who married Ephraim Lópes Pereira d'Aguilar, 2nd Baron d'Aguilar.
