Lord Arthur married his first cousin, Hon. Elizabeth Boscawen (bef. 1793 – 2 March 1872), daughter of George Boscawen, 3rd Viscount Falmouth, on 23 June 1808. They had three children:
Elizabeth Anne Somerset (2 August 1810 – 12 April 1835)
Arthur Edward Somerset (28 August 1813 – 9 September 1853), married his first cousin, Hon. Frances Boscawen, daughter of Rev. Hon. John Evelyn Boscawen, and had issue.
^Capt B.E. Sargeaunt, The Royal Monmouthshire Militia, London: RUSI, 1910/Uckfield: Naval & Military Press, nd, ISBN 978-1-78331204-7, pp. 103, 259, 285.