Permanent magnet synchronous machines (PMSM), synchronous reluctance machines (SynRM), and electrically excited synchronous machines (EESM), are used widely in the industry and transportation sectors. Often their rotors are equipped with conducting parts like permanent magnets, thick rotor laminations, real damper windings, a conducting sleeve or even have a solid rotor core. Such conducting ... [Show full abstract] elements do not allow applying standard AC-supply techniques for the inductance measurements due to the alternating flux induced by eddy currents. We propose a new technique for inductance measurement at standstill with a quasi-static voltage supply, which mitigates the eddy current phenomenon. The inductance is measured at several rotor positions over the complete electrical cycle, which allows to proceed with a harmonic spectrum analysis of the inductance variation. With this information, it is possible to estimate motor performance characteristics, such as optimum torque, voltage control, power factor, and torque ripple. The new technique is experimentally validated on a 12 kW axially laminated anisotropic solid-rotor high-speed SynRM. In principle, the method also suits to PMSMs, EESMs, and other possible synchronous machines (not verified in this paper). Experimental validation with a solid-rotor SynRM shows a good correspondence with the simulation. Furthermore, the torque computed using the measured inductance is very similar to the experimental one confirming the effectiveness of the method.