A non-contact low-frequency (LF) method for diagnosing the plasma surrounding a scaled model in a shock tube is proposed. This method utilizes the phase shift occurring after the transmission of an LF alternating magnetic field through the plasma to directly measure of the ratio between the plasma loop average electron density and collision frequency. An equivalent circuit model is used to analyze the relationship between the phase shift of the magnetic field component of LF electromagnetic waves and the plasma electron density and collision frequency. The applicable range of the LF method at a given plasma scale is analyzed. The upper diagnostic limit for the ratio of the electron density (units: m-3) to collision frequency (units: Hz) exceeds 1 × 1011, enabling an electron density exceeding 1 × 1020 m-3 and a collision frequency less than 1 GHz. The paper also assesses the feasibility of using the LF phase shift for plasma diagnosis. Diagnosis experiments were conducted on shock tube equipment using both the electrostatic probe method and LF method. By comparing the diagnostic results of the two methods, the inversion results were relatively consistent, thereby providing preliminary evidence for the feasibility of the LF method. The ratio of the electron density to the collision frequency has a relatively uniform distribution during the plasma stabilization time. The LF diagnostic path is a loop around the model, which is suitable for diagnosing the plasma that surrounds the model. Finally, the causes of diagnostic differences between the two methods are analyzed. The proposed method provides a new avenue for diagnosing high-density enveloping plasma.