Method for operating a synchronous machine, having the following steps: ascertaining a rotor angle of the synchronous machine by way of sensor-free rotor angle detection; determining a difference value between a rotor inductance of the synchronous machine in the pole axis direction and a rotor inductance of the synchronous machine in the pole gap direction in a coordinate system, fixed to the rotor, of the synchronous machine; discarding the ascertained rotor angle if an amplitude of the difference between the rotor inductance of the synchronous machine in the pole axis direction and the rotor inductance of the synchronous machine in the pole gap direction lies below a predefined limit value; and driving the synchronous machine using the ascertained rotor angle if the amplitude of the difference between the rotor inductance of the synchronous machine in the pole axis direction and the rotor inductance of the synchronous machine in the pole gap direction does not lie below the predefined limit value; wherein the step for ascertaining the rotor angle comprises applying high-frequency test voltage signals in the pole axis direction, measuring the system responses to the applied high-frequency test voltage signals and estimating an angle using the measured system responses; wherein the step for determining the difference value comprises applying high-frequency test voltage signals in a direction differing from the pole axis direction, measuring the system responses to the applied high-frequency signals and estimating an angle using the measured system responses; characterized in that the high-frequency test voltage signals for ascertaining the rotor angle and the high-frequency test voltage signals for determining the difference value have different operating frequencies. ascertaining a rotor angle of the synchronous machine by way of sensor-free rotor angle detection; determining a difference value between a rotor inductance of the synchronous machine in the pole axis direction and a rotor inductance of the synchronous machine in the pole gap direction in a coordinate system, fixed to the rotor, of the synchronous machine; discarding the ascertained rotor angle if an amplitude of the difference between the rotor inductance of the synchronous machine in the pole axis direction and the rotor inductance of the synchronous machine in the pole gap direction lies below a predefined limit value; and driving the synchronous machine using the ascertained rotor angle if the amplitude of the difference between the rotor inductance of the synchronous machine in the pole axis direction and the rotor inductance of the synchronous machine in the pole gap direction does not lie below the predefined limit value; wherein the step for ascertaining the rotor angle comprises applying high-frequency test voltage signals in the pole axis direction, measuring the system responses to the applied high-frequency test voltage signals and estimating an angle using the measured system responses; wherein the step for determining the difference value comprises applying high-frequency test voltage signals in a direction differing from the pole axis direction, measuring the system responses to the applied high-frequency signals and estimating an angle using the measured system responses; characterized in that the high-frequency test voltage signals for ascertaining the rotor angle and the high-frequency test voltage signals for determining the difference value have different operating frequencies.