A nested conical passive magnetic bearing is presented. The bearing consists of a nested conical rotor inside a conical stator, i.e. two coaxial tilted rings of permanent magnets, both with a rectangular cross section. Varying the cone or tilt angle of the rotor and stator we determine the rotor radius that provides the highest force for three different magnetization cases. For this optimal rotor radius, we show that the bearing with the highest volume normalized force also has the highest stiffness, and furthermore often also the highest varying stiffness with axial displacement. Finally, we show that a conical bearings with a tilt angle of 60° has an almost constant stiffness and a linearly varying force with axial displacement, making it ideal as a bearing.