  We present a cavity-electromechanical system comprising a superconducting
quantum interference device which is embedded in a microwave resonator and
coupled via a pick-up loop to a 6 $\mu$g magnetically-levitated superconducting
sphere. The motion of the sphere in the magnetic trap induces a frequency shift
in the SQUID-cavity system. We use microwave spectroscopy to characterize the
system, and we demonstrate that the electromechanical interaction is tunable.
The measured displacement sensitivity of $10^{-7} \, \mathrm{m} /
\sqrt{\mathrm{Hz}}$, defines a path towards ground-state cooling of levitated
particles with Planck-scale masses at millikelvin environment temperatures.
