Accurate vibration isolation and magnetic levitation are extremely important in the high-precision industry. Nowadays, high-performance vibration isolation and magnetic bearings based on permanent magnets are increasingly considered. This paper proposes the stiffness matrix necessary for the design of such a structure. The analytical force and stiffness expressions are derived for the cases where the conventional analytical expressions are difficult to solve and are compared with results from the Maxwell Stress method. With these adapted expressions it is possible to optimize planar bearing structures without having to correct for non-solving configurations.