Cables comprising a flexible core and formed of wound superconducting tape wrapped helically around the flexible core, as well as methods of producing such cables are disclosed. The superconducting tape is wrapped around a conductive layer comprising conductive material, providing mechanical cushioning and electrical stabilization for the superconducting material. When producing such cables, tension control techniques support the protection of the superconducting tape and hence degradation of the superconducting material is largely or entirely avoided.