From the mid 1970s to the early 1990s, Nina Høiberg was the leading female chess-player in Denmark. Eight times she won the Danish Women's Chess Championships: 1974, 1976, 1977, 1978, 1986, 1991, 1992, and 1993.
Nina Høiberg three times participated in the Women's World Chess Championship Interzonal Tournaments:
Nina Høiberg played for Denmark in the Women's Chess Olympiads:[4]
- In 1976, at first board in the 7th Chess Olympiad (women) in Haifa (+3, =3, -6),
- In 1978, at first board in the 8th Chess Olympiad (women) in Buenos Aires (+7, =6, -1),
- In 1988, at first board in the 28th Chess Olympiad (women) in Thessaloniki (+7, =4, -3),
- In 1990, at first board in the 29th Chess Olympiad (women) in Novi Sad (+7, =6, -1),
- In 1994, at first board in the 31st Chess Olympiad (women) in Moscow (+7, =5, -2),
- In 2002, at first board in the 35th Chess Olympiad (women) in Bled (+2, =3, -4).
Nina Høiberg played for Denmark in the European Team Chess Championships:[5]
- In 1992, at first board in the 1st European Team Chess Championship (women) in Debrecen (+3, =0, -5),
- In 2015, at first board in the 11th European Team Chess Championship (women) in Reykjavík (+2, =3, -3).
In 1985, she was awarded the FIDE Woman International Master (WIM) title.