Cooling muon beams in flight requires absorbers to reduce the muon momentum, accelerating fields to replace the lost momentum in the longitudinal direction, and static solenoidal magnetic fields to focus the muon beams. The process is most efficient if both the magnetic fields and accelerating fields are high and the rf frequency is low. We have conducted tests to determine the operating envelope of high-gradient accelerating cavities in strong static magnetic fields. These studies have already produced useful information on dark currents, magnetic fields and breakdown in cavities. In addition to continuing our program at 805 MHz, we are starting to test a 201 MHz cavity and are planning to look at a variety of appropriate geometries and materials. In parallel with these activities, we are supporting R&D on models and surface structure.