The preparation and characterization of gold contacts on polycrystalline YBa2Cu3O7−x ceramics that carry high currents and exhibit contact resistances of only 50 mΩ at room temperature are reported. By cooling the sample this resistance remains essentially constant until the superconducting transition temperature, Tc≂89 K, is reached. At Tc the contact resistance decreases like the resistivity of YBa2Cu3O7−x, reaching at T<Tc about 10 μΩ. This value is comparable to the intrinsic resistance of the contact material. Thus, below Tc, the contacts exhibit vanishing contact resistance at the metal–high‐Tc‐superconductor interface. Such low contact resistances may be extremely important for the technical application of the novel superconductors.