The invention relates to a method for metal coating the surface of high temperature superconductors with a copper-oxygen base structure. The aim of the invention is to achieve a method as above, which requires a low production complexity, serves for the production of contacts with a low electrical and/or thermal transfer resistance and which increases the stability of the metallization. Said aim is achieved whereby copper is applied to give low-ohmic contacts, and the linked achievement of a stable metallization between the HTS and the electrical and/or thermal coupling. Further advantageous effects are achieved with the method whereby the copper is applied in the form of copper alloys, in particular as copper-nickel or copper-zinc alloys. On applying the method it is furthermore of advantage for the creation of fine grained surface coatings to overlay the galvanic cell with a permanent and/or alternating magnetic field.