Medford was part of the 1985 FIFA U-16 World Championship held in China, the first FIFA World Cup tournament where Costa Rica ever appeared, and scored the first goal ever for his home country in this type of tournaments. He made his senior debut for Costa Rica in a February 1987 friendly match against South Korea and earned a total of 89 caps, scoring 18 goals. He represented his country in 37 FIFA World Cup qualification matches and played in two World Cups, Italy 1990 and Japan-Korea 2002. He scored a goal against Sweden in the 1990 World Cup, which resulted in qualification for the second round. He also scored the winning goal at the Azteca Stadium against Mexico in the qualification for the 2002 FIFA World Cup. The match, known as the "Aztecazo", is one of only two World Cup qualifiers that Mexico have ever lost on home soil. He also played at the 1995 UNCAF Nations Cup as well as at the 1991, 2000, and 2002 CONCACAF Gold Cups and the 1997 and 2001 Copa Américas. His final international was a June 2002 FIFA World Cup match against Turkey.