Proton therapy is a rapidly increasing modality to treat cancerous tumors, but large-scale implementation, and therefore widespread availability for patients, is hindered by the size and upfront investment for treatment facilities. Superconducting technology can enable more compact, and therefore more affordable treatment systems, by increasing the magnetic field in the magnets for the proton accelerator (typically a cyclotron) and in the beam guidance up, over, and into the patient (the gantry). In this article, we discuss research at Varian Medical Systems Particle Therapy GmbH on various superconducting technologies for potential application in future, more compact cyclotrons and gantries. We discuss which technologies are feasible, and to what extent. We demonstrate why certain conductor choices are made, and show the development of novel new conductor and magnet technologies that will be required to enable the next generation of cryogen-free, conduction-cooled compact treatment systems. We conclude that superconductivity is certainly required for the next generation of proton treatment systems, but also that the amount of compactness that can eventually be achieved is not solely determined by the magnetic field strength that is generated in the magnets.