In this paper, we propose a new method for the accurate estimation of frequencies and magnitudes of harmonics and interharmonics caused on the supply-side currents by an adjustable-speed drive. The proposed method consists of a three-step procedure in which Estimation of Signal Parameters by Rotational Invariance Technique (ESPRIT) and Prony high-resolution methods are properly applied together with theoretical formulas. The method guarantees high accuracy with acceptable computational effort. Numerical applications were made on a hardware PWM adjustable-speed drive, and comparisons were made between the results of the proposed method, results obtained by applying the traditional IEC standard approach, and results obtained by another high-resolution method proposed in the relevant literature. The numerical applications and comparisons demonstrated the superior effectiveness and efficiency of the proposed method.