A connection arrangement for electrically interconnecting the shields of so-called "cold-dielectric" superconductor cables in the context of a muiltiphase superconductive electrical link, each super-conductor cable comprising a central superconductor presenting superconductivity at cryogenic temperature, electrical insulation surrounding the central conductor, a shield surrounding the electrical insulation, and a cryostat surrounding said shield. According to the invention, the arrangement comprises a superconductive link between said shields, said superconductive link comprising a link superconductor and a cryogenic sheath surrounding said link superconductor, each of the two ends of said link superconductor being connected to a respective one of said shields by connection means that are both electrically and thermally conductive. The invention is particularly applicable to high voltage electricity.