Two-stage oil-free centrifugal air compressors can bring significant advantages and open new market opportunities for compressor manufacturers. One of the core technologies behind this compressor type is the high-speed (HS) electrical machine supported by active magnetic bearings (AMBs). In this paper, the requirements set by the compressor on the electrical machine design are presented. The design solutions aimed to satisfy these requirements are discussed. Two case studies illustrate possible design approaches for the target application with examples of a 120kW, 60000rpm induction machine with a solid rotor and a 225kW, 50000rpm permanent magnet synchronous machine (PMSM) with a full cylindrical magnet. The system design and simulation results are confirmed by measurements of a PMSM prototype.