This paper describes a detailed design of a 6 Tesla Nb3Sn superconducting racetrack coil designed for conduction cooling. We then describe a bench test pursued as a proof of concept for one winding of an actively-shielded, air core electric machine with superconducting field windings. Design selection from a previously computed pareto-optimal front as well as electromagnetic performance of the test coil is discussed. The winding and support structure design is discussed. Analysis of the thermal performance is carried out to verify required temperatures given the cryostat and cryocooler setup. Finally, a strain analysis is performed in order to verify that the superconducting windings are within an acceptable strain level to avoid mechanical breakage as well as excessive degradation of the critical surface. Additionally, the structural integrity of the support components is verified. Test procedures and preliminary results are described.