[en] A liquid helium cryostat of a size and construction unavailable commerically, was built for use in measuring the Q of several materials at milli-Kelvin temperatures. The design and testing of the cryostat is described as well as the design of the experiment vacuum chamber and adaptor for the dilution refrigerator insert. Theory, design, and testing are also discussed for the magnetic coils built to levitate the materials so as to isolate them and increase the measured Q. A four point suspension with capacitor end plates as the transducer was used to obtain preliminary Q measurements of 6061 aluminum alloy and single crystal silicon. Results are tabulated