The title of Baron Farnham was created in the Peerage of Ireland in 1756. The 2nd Baron was created Viscount Farnham (1760) and Earl of Farnham (1763), but these titles became extinct upon his death in 1779. His successor, the 3rd Baron, was again created Viscount Farnham (1781) and Earl of Farnham (1785), but these titles again became extinct upon the death of the 2nd Earl of this creation in 1823.

Barons Farnham (1756)

• John Maxwell, 1st Baron Farnham (d. 1759)
• Robert Maxwell, 1st Earl of Farnham, 2nd Baron Farnham (d. 1779)
• Barry Maxwell, 1st Earl of Farnham, 3rd Baron Farnham (d. 1800)
• John James Maxwell, 2nd Earl of Farnham, 4th Baron Farnham (1760-1823), elected a Representative Peer in 1816
• John Maxwell-Barry, 5th Baron Farnham (1767-1838), elected a Representative Peer in 1825
• Henry Maxwell, 6th Baron Farnham (1774-1838)
• Henry Maxwell, 7th Baron Farnham (1799-1868), elected a Representative Peer in 1839
• Somerset Richard Maxwell, 8th Baron Farnham (1803-1884)
• James Pierce Maxwell, 9th Baron Farnham (1813-1896)
• Somerset Henry Maxwell, 10th Baron Farnham (1849-1900), elected a Representative Peer in 1898
• Arthur Kenlis Maxwell, 11th Baron Farnham (1879-1957), elected a Representative Peer in 1908
• Barry Owen Somerset Maxwell, 12th Baron Farnham (1931-2001)
• Simon Kenlis Maxwell, 13th Baron Farnham (b. 1933)