We acknowledge financial support from (a) the Spanish Ministry of Science and Innovation MCIN/AEI through Grant No. PID2019-104670GB-I00 and (b) the Horizon Europe 2021-2027 Framework Programme (European Union) through the SUPERMEQ project (Grant Agreement No. 101080143). J.C.-S. acknowledges funding from AGAUR-FI Joan Oró grants (Grant No. 2024 FI-2 00143), Generalitat de Catalunya. W.W. acknowledges funding in part by the Knut and Alice Wallenberg Foundation through a Wallenberg Academy Fellowship, the QuantERA project CMON-QSENS!, and the European Research Council under Grant No. 101087847 (ERC CoG SuperQLev). G.H. acknowledges support from the Swedish Research Council (Grant No. 2020-00381). C.N. acknowledges support as a Serra Húnter Fellow. This research was funded in whole or in part by the Austrian Science Fund (FWF) (10.55776/esp525).

Data used for figures in "Modeling magnetically levitated superconducting ellipsoids, cylinders, and cuboids for quantum magnetomechanics"