Rapid transport current versus high magnetic field characterisation of high-irreversibility type II superconductors is important to maximise their critical parameters. HTS conductors are already used to produce insert coils that increase the fields of conventional magnets made from NbTi, (Nb, Ta)3Sn and Nb3Al wires. There is fundamental interest in the study of HTS tapes and wires in magnetic fields higher than 21T, the current limit of superconducting magnets producing a DC field. Such fields can be obtained by using pulse techniques. High critical currents cannot be routinely measured with a continuous current applied at liquid helium, hydrogen or neon temperatures because of thermal and mechanical effects. A newly developed pulsed magnetic field and pulsed current system which allows rapid Jc(B, T) measurements of the whole range of superconducting materials was tested with a multifilamentary NbTi wire in perpendicular and parallel orientations.