The main objective of the diploma thesis at hand was to measure the dependence of the critical current in melt-textured high-temperature superconductors on the angle between an external magnetic field and the crystallographic ab-plane of the superconductor, which is called transport current anisotropy. To that end, a suitable sample preparation method which includes sputter deposition of silver contacts had to be devised. Contact resistances of the order of 10E-9 Ohm*m^2 between these silver contacts and the superconductor were achieved by this method. The transport current anisotropy of melt-textured YBCO was measured at a temperature of 77 K and magnetic fields of up to 6 T. Anomalous transitions from the superconducting to the dissipative state were observed in some of the measurements and resulted in an unexpected shape of the corresponding anisotropy curves. These transitions were ascribed to the effect of Joule heating in the contact areas, as supported by the experimental data.