Superconducting magnetic bearings (SMBs) are usually composed of superconductors and permanent magnets (PMs). These SMBs are based on pinning forces between superconductors and PMs. In this paper, SMB-I composed of disk-shaped superconductor and SMB-II composed of doughnut-shaped superconductor are studied. To compare SMB-I with SMB-II, impulse responses in the vertical and horizontal directions are performed. Moreover, new types of SMB-III and SMB-IV are proposed. These SMB-III and SMB-IV are composed of superconductor and superconducting coils. To compare SMB-III with SMB-IV, impulse responses in the vertical and horizontal directions are studied. Then, natural damped vibration curves for impulse responses are observed. The damping coefficient for SMB-IV is larger than other SMB-I, SMB-II and SMB-III.