A localized area is at least partially contained within a perimeter of a shield ring formed by a closed superconducting current path of a material that is superconductive below a critical temperature. The shield ring is at least partially within a perimeter of a compensation coil that is coupled to a current source. One or more measurement devices are responsive to magnetic fields in the vicinity of the localized area, allowing compensation by controlling current to the compensation coil. A heater can raise temperature of the shield ring out of a superconducting condition.