He is the recipient of numerous honors and awards including:

• Virginia Colliers Chamber Music Award, Washington 1955
• Havana Lyceum Publicatin Award, La Habana, 1957
• Andrew Mellon Fellowship, University of Pittsburg, 1963
• Award of Merit, Atheneum of Buenos Aires, 1973
• Distinguished Professor Award, California State University, Northridge, 1974
• National Federation of Music Clubs Award, Washington, 1975
• Juan J. Remos Award, Miami, 1978
• City of Los Angeles Commendation, Office of the Mayor, Los Angeles, 1978 and 1993
• California State Senate Commendation, Sacramento, 1979
• Honor Distinction for Creativity, Patronato José Martí, Los Angeles, 1979
• Certificate of Merit, National Association of Composers, U.S.A., Los Angeles, 1980
• Award of Merit, Masonic Lodge No. 30, Los Angeles, 1981
• City of Los Angeles Commendation, Office of the Fourteenth District, Los Angeles, 1982
• Creativity Award, California State University, Northridge, 1984 and 1991
• Fulbright Research Award, Washington/Rio de Janeiro, 1985
• José de la Luz y Caballero Award, Miami, 1989
• Certificate of Recognition, California State Senate, Sacramento, 1991
• Biographical Honor Award, International Biographical Centre, Cambridge, 1993
• FACE Award, Facts about Cuban Exiles, Miami, 2000
• Cuban Cultural Heritage Foundation Prize, Coral Gables, 2004
• Warren Lifetime Achievement Award, Cintas Foundation, New York, 2010
• Ignacio Cervantes Award and Medal, Cuban Cultural Center, New York, 2012
• Imperial Hispanic Order of Charles V, 2018
• Premio Herencia Cubana Por Toda Una Vida De Creatividad Musical ("Cuban Heritage Lifetime Award"), Los Angeles, 2019
• Community Hero Award ("Premio Héroe de la Comunidad"), Los Angeles Dodgers, 2019
• CUBADISCO Award for the album Cuba: The Legacy, La Habana, 2021

Honors for his contributions to contemporary music, in particular to Latin American music include:

• Medal of the Order of the Sociedad Económica de Amigos del País, Cuba, 1956
• Medal of the Order of Eloy Alfaro, Colombia, 1961
• Medal of the Order of the Sun, Perú, 1969
• Medal of the Order Gabriele D’Annunzio, Italy, 1974
• Medal of the Order of Vicente Emilio Sojo, Venezuela, 1985
• Chevalier de l’Ordre Militaire et Souverain du Temple de Jerusalem (Templar Knights), Scotland, 1991