He played eight matches for the Denmark national team, and was selected for the 1986 World Cup and 1996 European Championship squads.

[9] He trained countless goalkeepers in the Danish Superliga, both individually but also firmly attached to clubs in the league.

He made his senior debut in 1977 as an amateur (later to become semi-professional, and eventually full-time-professional), and was an understudy to Denmark national team goalkeeper Mogens Therkildsen, as OB won the 1977 Danish championship.

The following years he established himself as OB's starting goalkeeper, and debuted for the Denmark under-21 national team in March 1979.

Høgh replaced Troels Rasmussen as starting goalkeeper when Denmark beat West Germany 2–0 and advanced to the knock-out stage.

In the round of 16 against Spain, Høgh conceded four goals to Spanish striker Emilio Butragueño, as Denmark lost 5–1 and was eliminated from the tournament.