Having amassed a record of 28–2 with 10 knockouts, Robinson Garcia challenged Isidro Martinez, 19-4-1, for the Latin American Super-Featherweight (Junior-Lightweight) title.
Two weeks after, Robinson Garcia held his first fight abroad, and first in the United States, when he faced Bobby Rogers on March 11 at the Auditorium, Miami Beach, losing that encounter by a ten-round decision.
Robinson Garcia lived in Mexico for one month, before returning to Cuba to face Jose Napoles a second time: on June 3, 1961, he again went ten rounds with the future world Welterweight champion and International Boxing Hall of Fame member, but once again dropped a points decision.
Fidel Castro soon abolished professional boxing in Cuba, however, and this would be Robinson Garcia's last presentation as a boxer in his home country.
Robinson Garcia began 1963 by fighting against another world champion and future International Boxing Hall of Fame member, Eddie Perkins, at the Palais de Sports, losing a ten-round unanimous decision.
On April 10, he knocked out Kid Tano, 45-5-6, in six rounds at the Canary Islands and then, only 11 days later, he held Italy's Carmelo Bossi, a future world champion, to a ten-round draw at Barcelona.
Robinson Garcia gave Durán a relatively close fight but still lost by unanimous ten-round decision with scores of 99–93, 98-94 and 98–96, all in favor of the Panamanian.
Robinson Garcia went 1-4 the rest of that year, facing, among others, Esteban De Jesus in San Juan, Puerto Rico, to whom he dropped a ten-round decision on July 8.
On March 29, he boxed the future ranked challenger, Puerto Rican Sandy Torres at Tampa, Florida, and lost a ten-round decision.
On July 17, he boxed future WBC world Junior Welterweight Champion Saoul Mamby at the Miami Beach auditorium and lost a ten-round decision as well.
He faced, among others, Mexican Marcos Geraldo (who'd later last ten rounds against Sugar Ray Leonard and Marvelous Marvin Hagler) on January 23 at the Silver Slipper Hotel in Las Vegas, Nevada, upsetting Geraldo by a fourth-round knockout win; then-undefeated Sugar Ray Seales on February 13 also at the Silver Slipper Hotel, losing by ten-round decision; Puerto Rican Josue Marquez (who had recently fought Antonio Cervantes for his world Junior Welterweight title) only five days after the Seales fight, losing by ten-round decision at San Juan; future Alexis Arguello world Junior Lightweight title challenger Arturo Leon, whom Robinson Garcia defeated by six-round decision at the Caesars' Tahoe in Stateline, Nevada, on April 18; Eddie Perkins again only nine days after the win against Leon-a ten-round unanimous decision loss at Tucson, Arizona; and future Angel Espada world Welterweight title challenger Johnny Gant, who obtained a ten-round decision win over Robinson Garcia on July 18 at Baltimore, Maryland.
Robinson Garcia had five extra fights apart from these in 1974, going 5–0 with 3 knockouts against lesser opposition, to finish 1974 winning 11 of 15 bouts held that year.
Nevertheless, among those five bouts was one against future Leonard world title challenger Larry Bonds, who outpointed Robinson Garcia over ten rounds at Las Vegas on February 26, future three time world champion and International Boxing Hall of Fame member, the then-only 16 years old Wilfred Benítez, who beat Robinson Garcia by ten-round decision on June 9 at the Ramon Loubriel Stadium in Bayamon, Puerto Rico-(sometimes incorrectly said to be in San Juan); and Adriano Marrero, a Dominican who would later challenge Antonio Cervantes unsuccessfully for Cervantes' WBA world Junior Welterweight title and who beat Robinson Garcia by a 10-round decision on August 5.
He went 1-5-1 during that span, losing to former undisputed world Welterweight Champion Billy Backus by a ten-round unanimous decision on April 3 at Utica, New York; to Rafael Rodriguez on points in 10 on May 5 at Minneapolis, Minnesota; to former and future WBA world Welterweight title challenger Clyde Gray by ten round unanimous decision on September 2 at Halifax, Nova Scotia; and to Willie "The Worm" Monroe by a seventh-round technical knockout December 3 at Rochester, New York.
He lost twice that year, including his last bout, on February 25, to contender Paul Payen, 17-1 coming in, on a ten-round decision at Hainaut, Belgium.