	In 1984 Melrose received the Bôcher Memorial Prize for his work on scattering theory. Since 1986 he has been a Fellow of the American Academy of Arts and Sciences. For the academic year 1992–1993 he was a Guggenheim Fellow. He was in 1978 an invited speaker ("Singularities of solutions of boundary value problems") at the ICM in Helsinki and in 1990 a plenary speaker ("Pseudodifferential operators, corners and singular limits") at the ICM in Kyoto.