During his dogeship, Dandolo was married to a woman named Contessa Minotto, to whom he delegated authority over his commercial and private affairs along with his brother, Andrea, and assumed friend Filippo Falier of the San Tomà parish, before he departed on a political trip to Constantinople with his brother, Giovanni, in 1183. Contessa's identity is debated, and it is often thought that she may have been a member of the Minotto clan though the veracity of this claim is inconclusive.