The dynamic properties of a ring-shaped superconducting magnetic bearing used in textile machines were studied for a micrometer displacement range. Therefore, a new measurement setup was designed that allows to excite the freely levitating magnet ring in a defined direction with small excitation amplitudes. Here, we focus on radial and axial excitations with amplitudes between 2 μm and 30 μm. The data were analyzed by a fast Fourier transformation approach. The resultant excitation response was fitted by the transfer function of a spring-mass-damper system under harmonic force excitation, which gives the stiffness and damping coefficient for the particular excitation direction. The analysis shows a minor stiffness increase with decreasing excitation amplitudes in radial as well as in axial direction. At the same time, no clear trend was found for the damping coefficient. In contrast to other bearing designs, the studied ring-shaped bearing exhibits a ratio of 3 between the axial and radial stiffness.