Superconducting cables employ one or more superconducting tapes wound around a former. A compact superconducting cable is configured using a former having a small diameter, e.g., less than 10 millimeters. A flexible superconducting cable is configured with a former made of a flexible material. Superconducting tape conductors are wound around the former, with the superconducting layer in compression on the inside of the wind turns of the wind, to prevent irreversible damage to the superconductor. A layer of solder is on the superconducting tape(s) or solder sheaths are wound between tape conductors in each layer. The one or more solder layers or sheaths are melted to cause the solder to flow within the structure, to bond some or all of the superconducting tape conductors together and form a mechanically strong cable with an enhanced level of electrical connectivity between tapes in the cable.