Methods and apparatuses to provide improved auxiliary damping for superconducting bearings in superconducting levitation systems are disclosed. In a superconducting bearing, a cryostat housing the superconductors is connected to a ground state with a combination of a damping strip of material, a set of linkage arms to provide vertical support, and spring washers to provide stiffness. Alternately, the superconducting bearing may be supported by a cryostat connected to a ground state by posts constructed from a mesh of fibers, with the damping and stiffness controlled by the fiber composition, size, and mesh geometry.