Superconducting (SC) motors are nowadays being proposed for zero-emission aviation. Their specific power and power density are under various studies to assess their feasibility in such an application. This paper preliminarily assesses two novel armature winding concepts for SC motors, based on the concentric-racetrack-coil (CRC) concept and the direct-liquidcooling (DLC) technology. The two armature winding concepts result in conceptual designs of a fully SC motor (FSCM) and a partially SC motor (PSCM), respectively. The specific power and power density of the conceptual designs are assessed by comparing them with aviation-oriented goals and with other reference motor concepts. The results show that the CRC SC winding concept for FSCMs can reach and even exceed the higher specific power goal of 25 kW/kg. The DLC copper winding concept for PSCMs is quite close to the lower specific power goal of 12.7 kW/kg. Improvements in the PSCMs and better utilization of their materials can be expected to fulfill the lower goal. Then the copper armature winding with CRC and DLC will be a potential solution considered for applying PSCMs to electrifying aircraft.