At the start of 1989 Branković ran an indoor personal best over 200 metres of 21.24 seconds in Turin – this mark remains the Serbian national record. He narrowly missed out on a medal in the 400 m at the 1989 IAAF World Indoor Championships, coming in fourth place behind Spaniard Cayetano Cornet. That same year he completed a Yugoslavian title double over 200 m and 400 m. He retained his 200 m title the following year and competed for his nation on home turf for the 1990 European Athletics Championships in Split. He ran a career best of 45.30 seconds for the 400 m to qualify for the final (a time which is the current Serbian record) and finished sixth overall. As part of the relay team he helped the Yugoslavian men reach fifth place. Another Yugoslavian relay record came for him at the 1991 World Championships in Athletics: competing in a team which also featured Dejan Jovković, Nenad Đurović and Mačev, he reached the final of the competition with the country's first sub-three-minute mark for the event (2:59.95 min). The Yugoslavian team came fourth in the relay final, just over two tenths of a second behind bronze medallists Jamaica.