Miami won national championships in 1983, 1987 and 1991 with Orange Bowl victories. The only loss for Miami with a chance to share the National Championship was when they were defeated 24-17 by Nebraska in the 1995 Orange Bowl.
Miami beat Nebraska 31-30 in the 1984 Orange Bowl in one of the biggest upsets in college football history to win its first National Championship. Nebraska was about a 10.5 to 11 point favorite in the 1984 Orange Bowl.
The 1983 Nebraska team was considered by many to be the greatest in College Football history at the time.