After two years as a backup at Albacete Conejo returned to Costa Rica with C.S. Herediano, retiring the following year after one season with Ramonense, aged 37. He received international recognition during the 1990 FIFA World Cup: appearing in three matches with two goals conceded, his heroic saves against Scotland, Brazil and Sweden helped Costa Rica reach the second round, but he did not appear in the round-of-16 encounter against Czechoslovakia because of an injury, and his team was eliminated; France Football magazine named him the best goalkeeper of the tournament.
Subsequently, Conejo worked with the national team as goalkeepers' coach. In his country he is highly regarded by fans, even though he never played for any of the top clubs in the nation.
In 2009, IFFHS named Conejo the 34th best goalkeeper of the world for the period 1987–2008, and the seventh in Latin America.