I propose to experimentally investigate micro-magnetomechanical systems made of superconducting particles with size in the micron range, levitated in a magnetic trap. These systems have been recently suggested as a possible platform for the exploration of the macroscopic limits of quantum mechanics. I will illustrate the advantages of this approach, compared to other techniques like matter-wave interferometry or optically levitated nanoparticles. In particular, it is argued that conventional decoherence can be radically suppressed by operation at subkelvin temperature, enabling to achieve a regime where spontaneous wavefunction collapse models may become testable in a relevant range of parameters. I will introduce some specific levitation schemes and discuss experimental prospects and potential issues.