In the framework of the SwissFEL project at the Paul Scherrer Institute (PSI), a Hall probe bench is being developed for the high-precision magnetic characterization of the insertion devices for the ATHOS soft X-ray beamline. For this purpose, a novel three-axis teslameter has been developed, which will be placed between the undulator and its outer shell in a very limited volumetric space of 150 x 50 x 45 mm. Together with a Hall probe at the center of the cross sectional area of the undulator, the setup will traverse along the undulator length on a specifically designed rig with minimal vibrations. This teslameter has all the analog signal conditioning circuitry for the Hall probe and also has on board 24-bit digitization. The instrument also handles an interface to a linear absolute encoder. The old instrumentation used only had analog signal conditioning circuitry whilst digitization was done off board. The new instrument also provides a very accurate magnetic field map in the µT range with simultaneous readings from the position encoder at an accuracy of ±3 µm. In this paper, a series of tests are described, which were performed at PSI in order to establish the measuring precision and repeatability of the instrument.