After Fidel Castro came to power, thousands of Cuban exiles left the island and settled in Miami. The president of the University at that time, Henry King Stanford, opened the doors to the new exiles and established a series of programs to help them:
• The UM School of Medicine established the Cuban Refugee Program to prepare Cuban physicians for the Educational Council for Foreign Medical Graduates.
• The University also provided training courses for Cuban lawyers through a U.S. Department of Health, Education and Welfare grant and established the Cuban Teachers Program to train Cuban teachers for jobs in the Dade County Public School system.
• In 1965 UM established the Cuban Cultural Center at the Koubek Memorial Center to help recently arrived Cuban exiles adjust to life in the United States. Many refugees participated in the vocational and cultural programs offered at the Center. To this day, the Koubek Center continues to provide cultural and educational programs to the community.
• The Federation of Cuban Students was founded in the late 1960s. By 1970 there were approximately 1,500 Cuban exile students attending the University. The Federation of Cuban Students is still active today and promotes cultural awareness of Cuban traditions, history, music, and current events. The president for 2007-2008 is Elena Smukler.
The University of Miami has awarded honorary degrees to 16 Cubans since 1928; these have included the then-president of Cuba, Ramon Grau San Martin, in 1949, to beloved Salsa queen Celia Cruz in 1999, and most recently to Cuban dissident and journalist Raúl Rivero Castañeda.