This paper aims to provide some useful instructions to electromagnetic design of high-speed permanentmagnet machines. In this paper, the electromagnetic design procedure is illustrated with a 2 poles 40,000 rpm prototype machine. In order to determine a rotor structure with good performance, rotor design including rotor structure, pole arc and magnetization direction of magnets are analyzed respectively. On the other hand, two machines with different stator cores but same rotors are studied. And a novel method of stator winding design is provided to have more options for the design by increasing number of parallel branches. Finally, the influence of stator slot opening and number of segmentations in magnets to rotor eddy-current loss are discussed. Smaller stator slot opening would reduce the rotor eddy-current loss, but it brings some processing technic problems. And segmentation in magnets would reduce the eddy-current loss in magnets only.