This work proposes a novel contactless vibration damping and thermal isolation tripod platform based on Superconducting Magnetic Levitation (SML). This prototype is suitable for cryogenic environments, where classical passive, semi active and active vibration isolation techniques may present tribological problems due to the low temperatures and/or cannot guarantee an enough thermal isolation. The levitating platform consists of a Superconducting Magnetic Levitation (SML) with inherent passive static stabilization. In addition, the use of Operational Modal Analysis (OMA) technique is proposed to characterize the transmissibility function from the baseplate to the platform. The OMA is based on the Stochastic Subspace Identification (SSI) by using the Expectation Maximization (EM) algorithm. This paper contributes to the use of SSI-EM for SML applications by proposing a step-by-step experimental methodology to process the measured data, which are obtained with different unknown excitations: ambient excitation and impulse excitation. Thus, the performance of SSI-EM for SML applications can be improved, providing a good estimation of the natural frequency and damping ratio without any controlled excitation, which is the main obstacle to use an experimental modal analysis in cryogenic environments. The dynamic response of the 510 g levitating platform has been characterized by means of OMA in a cryogenic, 77 K, and high vacuum, 1E-5 mbar, environment. The measured vertical and radial stiffness are 9872.4 N/m and 21329 N/m, respectively, whilst the measured vertical and radial damping values are 0.5278 Nm/s and 0.8938 Nm/s. The first natural frequency in vertical direction has been identified to be 27.39 Hz, whilst a value of 40.26 Hz was identified for the radial direction. The determined damping values for both modes are 0.46% and 0.53%, respectively.