The increasing share of power electronic (PE) devices in public electricity networks has increased the chance of harmonic instabilities, which are caused by the interaction of the device control with the network impedance. Usually, the detailed internal design of PE devices is not available and only measurement-based black-box approaches are feasible for the analysis of harmonic instabilities. A major drawback of such black-box approaches is the need for expensive programmable grid simulators. To overcome that issue, this article proposes a new approach to identify the sensitivity of a PE device for harmonic instabilities, which solely requires two air coils and which can simply be connected to any available power supply including the low voltage (LV) network. By systematically increasing the resulting inductance of air coils, the proposed method is able to identify the frequency regions that are critical with regard to the harmonic stability of the PE device. Critical frequency regions are determined by analyzing the measurement results in time-frequency domain using the estimation of signal parameters via rotational invariance techniques (ESPRITs). The proposed method is applied to a commercially available single-phase photovoltaic (PV) inverter. The critical frequency region has been determined at around 500 Hz, which is confirmed by formal stability analysis.