A vacuum magnetic field from a superconducting coil set for a single cell minimum-B mirror-based fission-fusion reactor is computed. The magnetic field is optimized for MHD stability, ellipticity and field smoothness. A recirculation region and wide magnetic expanders on both sides are provided to the central mirror cell. A coil set producing this field is computed which consists of circular and quadrupolar coils. Basic scaling assumptions are made for the coil dimensions, based on a maximum allowed current density of 1.5 kA/cm2 for superconducting coils. Sufficient space is available for a fission mantle. The field produced by the coils is checked for MHD plasma stability and maximum ellipticity. The resulting confinement region is 25 m long with a 40 cm midplane plasma radius.