The levitation forces on metal spheres in magnetic fields of axial symmetry are derived theoretically. Criteria for stability of the center of mass are obtained. It is shown for nonmagnetic samples that the desirable coil configurations are those which provide a constant field gradient along the symmetry axis. The formalism is applied to model coils of axial symmetry as an approximation to real spiral coils. An exact formula is derived for the axial component of the magnetic field on the axis of a spiral coil wound on the surface of a cone, and the transverse fields are evaluated approximately.