He 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. Medford also represented Costa Rica's national squad 89 times, playing 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, Costa Rica's best World Cup performance. He also scored the winning goal at the Azteca Stadium against Mexico in the qualification for the 2002 World Cup, one of only two home World Cup qualifiers that Mexico have ever lost.
After retiring from professional football in 2003, he entered coaching. He first coached Deportivo Saprissa with great success, where he has won several championships, including 2 national tournaments, the Uncaf Cup and the CONCACAF Champions Cup, giving Saprissa the right to compete in the second FIFA Club World Championship Toyota Cup in Japan, in December 2005, in which Saprissa finished 3rd.
As of October 28, 2006, the Costa Rican Football Federation, or Federación Costarricense de Fútbol, announced him as the new head coach for the Costa Rica national football team. He was sacked on 28 June 2008 after a string of poor results and only a few wins, and showing unprecedent bias in favor of his old former players of Saprissa.
He took the reins of Club León for the Clausura 2009 season. His first game as head coach was against Tampico Madero, ending in a 1-1 tie. He was fired as manager by the president of the club owing to poor results in the pre-season and the season itself.
After leaving Club León Medford decided to take a break in coaching and decided to work as an administrator/manager. He signed with Brujas F.C., a club team from the capital San Jose. He signed to be the club administrator/manager. After two seasons Hernan decided to resign due to the lack of good results from the club, among other disagreements with the board of directives. In 2010 Hernan Medford signed with Limon Futbol Club, a club team from the province of Limon. He signed also as an administrator. The team seemed to have benefited from his previous experience as administrator. In June 2011 Carlos Pascal the team’s chairman was arrested due to accusations of drug trafficking leaving the club without a president. Medford tried to help the team survive this set back since without Pascal the team was left without financial support. Medford endured a difficult season with Limon F.C. In August 2011 Medford resigned, claiming it had nothing to do with the financial problems the club had suffered, but because of personal decisions.
In May 2013, he was unveiled as the new manager of Honduran giants Real España. Under his direction Real España became the 2013 champion of the "Catracha" league.