[en] The accelerators must take the muon beams from ∼ 100 MeV to 2 TeV energies within the muon lifetime for a 4 TeV energy muon collider. These constraints plus the muon decay heating seriously challenge the designs of the superconducting RF (SRF) cavities and magnets in the accelerators and collider ring. The multiple superconducting recirculation linac and the very rap8id-cycling superconducting synchrotron approach are both studied. The authors briefly introduce the technical considerations and preliminary designs of the SRF systems and magnets