An important challenge in the design of air-core superconducting machines is the containment of the magnetic fields within the electric machine. Current solutions result in large reductions of the high power density achievable through the use of superconducting windings. To address this challenge, an actively shielded electromagnet design, an approach commonly used in MRI magnet designs, is considered. This topology utilizes a set of main coils to produce armature MMF, while including another set of oppositely excited compensating coils to mitigate the fields radiating outside the machine. This approach eliminates or reduces the use of steel in a passive magnetic shield, allowing for very high power density machines. Furthermore, a multi-objective optimization scheme is introduced to minimize two competing objectives, superconducting coil usage and machine radius. Results show a 32% decrease in machine radius with a 33% increase in coil size.