One of Short's best tournament results came at the Amsterdam VSB tournament in 1991 when he tied for first place with Valery Salov ahead of both Kasparov and Karpov. In April 2003 he won the Hunguest Hotels Super Chess Tournament held in Budapest ahead of Boris Gelfand, Judit Polgar and Peter Leko among others (Polgar and Leko were in the world's top ten at the time).
In recognition of his chess accomplishments, he was awarded the honorary OBE (Order of the British Empire) title.
In the January 2004 FIDE rating list, Short was ranked number 17 in the world with an Elo rating of 2702, making him England's number two (behind Michael Adams).