A superconducting magnet has been constructed for the determination of excited-state g-factors of fission products through perturbed angular correlation measurements at the separator JOSEF. The system contains a channel at room temperature which allows the rapid transport of radioactive samples with a tape device into the centre of the magnet. Thus experiments on the γ radiation from short-lived β- decaying nuclei are possible. The coils of the magnet have been built by Oxford Instruments Ltd while the cryostat has been designed and manufactured in the central workshop of the Kemforschungsanlage Jülich. The maximum field strength is 6.54 T at a current of 59 A and the homogeneity is better than one percent for an area with a radius of 0.5 cm at the centre of the magnet. The liquid helium consumption is only 0.3 l/h. The magnet has been used for the determination of the g-factors of the 2 1+ states in 102Mo and 104Mo.