She was born in Melbu in Hadsel Municipality, a daughter of Olaf Røstvig and Sigrid Elise Larsen.
[1][2] Røstvig was a student during the German occupation of Norway, and took part in the civil resistance.
[3] From August 1944 to May 1945 she published the illegal weekly newspaper Frihet og fred (34 issues), along with two other women.
[4] Røstvig obtained a doctorate in historical treatise on English poetry in the 17th-century from the University of California.
In her book Configurations (1994), she explored the formal elements of European poetry, with special focus on the works of Edmund Spenser to John Dryden.