A description is given of the cryogenic part of an electron paramagnetic resonance (EPR)/ferromagnetic resonance (FMR) spectrometer using Ka-band (26.5-40 GHz) and U-band (40-60 GHz) frequencies for resonance measurements on large magnetic thin-films. The unit has two cryostats; the first has a room-temperature vertical inlet tube giving access to the center of the superconducting magnet. This cryostat can be rotated around the central axis of the inlet tube and enables rotation of the magnetic field around a fixed sample, placed in the center of the magnet. This cryostat also contains a superconducting Helmholtz-like coil (up to 5 T at the center). Also there is a flow cryostat placed freely in the inlet tube of the first cryostat. This cryostat is used to cool the EPR/FMR sample. The discussion of the EPR/FMR presented places emphasis on the construction of both cryostats, as well as on the design calculations and construction of the superconducting magnet coil. The calculations are compared with experimental data.