Cuéllar won the Colombian championship nine times: in 1941, 1946, 1953, 1955, 1956, 1957, 1959, 1961, and 1971. He played for Colombia in six Chess Olympiads: 1954, 1956, 1958, 1964, 1970, and 1972. He won individual silver medal at first board (+12 –2 =4) in the 16th Olympiad at Tel Aviv 1964.
In 1952, he tied for 3rd-4th in Mar del Plata (Julio Bolbochán and Héctor Rossetto won). In 1953, he took 5th in Mar del Plata (Svetozar Gligorić won). In 1957, he took 7th in Mar del Plata (Paul Keres won). In 1958, he tied for 2nd-3rd with William Lombardy, behind Oscar Panno, in Bogotá.
In 1961, Cuéllar won in Caracas (zonal). In 1962, he placed 22nd at the Stockholm Interzonal, defeating both Efim Geller and Viktor Korchnoi in individual games. In 1966, he took 7th in Havana (Eleazar Jiménez won). In 1967, he tied for 19-20th in Sousse (interzonal; Bent Larsen won). In 1969, he tied for 1st with Boris De Greiff in Bogotá. In 1970, he took 7th in Bogotá (Henrique Mecking won). In 1970, he took 14th in Caracas (Lubomir Kavalek won). In 1973, he took 18th in Leningrad (interzonal; Anatoly Karpov and Viktor Korchnoi won). In 1980, he tied for 4-5th in Bogotá (Joaquin Gutierrez won).
- Gaige, Jeremy (1987), Chess Personalia, A Biobibliography, McFarland, p. 80, ISBN 0-7864-2353-6
- Cuéllar Gacharná, Miguel team chess record at olimpbase.org
- Keene, Raymond (1977), "Cuéllar, Miguel", in Golombek, Harry, Golombek's Encyclopedia of Chess, Crown Publishing, p. 82, ISBN 0-517-53146-1
- Sunnucks, Anne (1970), The Encyclopaedia of Chess, St. Martin's Press, p. 93, LCCN 78106371
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