Romer attended Trinity Hall at Cambridge University and was Senior Wrangler in 1863, and also won the Smith's Prize in that year. From 1865 to 1866, he was a professor of mathematics at Queen's College, Cork, but was called to the bar in 1867. He became QC in 1881, and a bencher of Lincoln's Inn in 1884.
Romer was sworn a Privy Councillor in 1899, and elected a Fellow of the Royal Society in the same year. He was appointed Knight Grand Cross of the Order of the Bath (GCB) in the New Year Honours list 1 January 1901, and was invested by King Edward VII in February the same year.
In 1864 he married Betty Lemon, daughter of Mark Lemon, editor of Punch. Their son was Mark Romer, Baron Romer and their grandson was Sir Charles Robert Romer; both were also Lords Justice of Appeal. Their daughter Helen Mary married future Lord Chancellor Frederic Maugham.
- GCB : Knight Grand Cross of the Most Honourable Order of the Bath - 1 January 1901 - New Year Honours list
- The London Gazette: . 8 January 1901. Retrieved 11-10-2012.
- "Court Circular" The Times (London). Thursday, 14 February 1901. (36378), p. 6.
- "The Royal Commission on South African Hospitals". PMC 2400194.
- "Thomas Carlyle Parkinson, M.D. (Sydney)". PMC 2318341.
- "Romer, Robert (RMR859R)". A Cambridge Alumni Database. University of Cambridge.
- MacKinnon, Frank Douglas; (rev.) Patrick Polden (2004). "Romer, Sir Robert (1840–1918)". Oxford Dictionary of National Biography. Oxford University Press. Retrieved 19 February 2011.