A zero-field cooled superconducting shield is proposed to realize a high-field (3-4 T) septum magnet for the Future Circular Collider hadron-hadron (FCC-hh) ring. Three planned prototypes using different materials and technical solutions are presented, which will be used to evaluate the feasibility of this idea as a part of the FCC study. The numerical simulation methods are described to calculate the field patterns around such a shield. A specific excitation current configuration is presented that maintains a fairly homogeneous field outside of a rectangular shield in a wide range of field levels from 0 to 3 Tesla. It is shown that a massless septum configuration (with an opening in the shield) is also possible and gives satisfactory field quality with realistic superconducting material properties.