Adelaer was first married in 1656 in Hoorn (Netherlands) to Angelica Sophronia (died before 1661) and secondly in 1662 in Amsterdam with Anna Pelt (1640–1692). Descendants of Cort Adeler became members of a Danish noble family when Admiral Cort Adeler was converted into position of nobility on 7 February 1666. Cort Adeler's older son, Sivert Cortsen Adeler was a Danish naval officer. His younger son,
Frederik Christian Adeler, was a Danish Councilor and Prefect in
Zealand Diocese and his grandson,
Frederik Adeler (1700–1766) was a government official and landowner, who served as a County Governor of several counties in Norway and Denmark. His daughter Susanne Elisabeth Adeler was married to Frederik Eiler Giedde, til Nordskov og Hindemae (1641–1717), a son of
Ove Ghedde. Another daughter, Sophie Amalie Adeler (1661–1734), was married to count Adam Friederich von Trampe, til Løgismose (1650–1704). Members of the family have been associated with a number of Danish estates including
Ulstrup Slot. The
Cort Adeler House, Cort Adeler's former home in Copenhagen, located at
Strandgade 22 in
Christianshavn, is a listed building. ==Legacy==