Rational function approximations are widely used for the modelling of frequency-dependent effects in power system components. This paper proposes to use optimization by the damped Gauss–Newton method to improve the accuracy of rational approximations calculated by three mainstream fitting techniques: Bode's asymptotic approximation, Sanathanan–Koerner iteration, and vector fitting. The optimization method is described in detail along with an outline of the numerical implementation. The proposed methodology is demonstrated for a synthetic example for the modelling of a measured reactor frequency response and for the rational fitting of the frequency-dependent parameters corresponding to a single-phase transmission line. In this example, we also present the impact of the optimization enhancement on the final time domain responses.