When Bayern's amateur team coach Hans-Dieter Schmidt later became manager of German club Hannover 96, he remembered Schjønberg and offered him a contract.

[3] He won his first trophy as a senior player, when the club surprisingly beat top flight Borussia Mönchengladbach, to win the 1991–92 DFB-Pokal.

The game ended in a penalty shoot-out, where Schjønberg scored the deciding kick to secure the triumph for Hannover 96.

[4] Unhappy with the new contractual offer from Hannover 96, Schjønberg looked ready to move back to Denmark to play for OB in summer 1992.

It was OB's greatest European result, as the club eliminated Spanish giants Real Madrid (against whom Schjønberg scored in the first leg)[6] before being narrowly defeated by Italian side AC Parma in the quarter-finals.

He scored the club's very first goal of the 1997–98 season, in the opening game against defending champions Bayern Munich.

Ten minutes before the final whistle, Schjønberg headed the ball in after a cross from Swiss midfielder Ciriaco Sforza and secured a 1–0 win.

This victory was the beginning of Kaiserslautern's fairytale, and Schjønberg went on to play 32 of 34 league games and to score four goals, as the club became the first ever 2.

Returning to Kaiserslautern after the 1998 FIFA World Cup, Schjønberg was heavily injured early in the 1998–99 season.

In September 1998, Schjønberg collided with VfL Bochum goalkeeper Thomas Ernst, and broke his shinbone.

By the half-time break, Gospodarek had suffered an injury of his own, and with no more goalkeepers selected for the match squad, Schjønberg took over the keeper's gloves.

He crowned his achievement with a saved penalty kick, when he held the shot from Alexander Iashvili in the 84th minute.

Schjønberg made his debut for the Denmark national team in the 1995 King Fahd Cup in January 1995.

The last group match against the Czech Republic on 21 June 2000, would be Schjønberg's last game for the national team.

He moved to Denmark in July 2004, to coach Danish Superliga club Herfølge BK, alongside his good friend Allan Nielsen.

When Neururer was fired in September 2006, Schjønberg deputised as head coach for a single DFB-Pokal match, where Hannover 96 eliminated Dynamo Dresden.