Single-tuned passive filters offer reasonable mitigation for harmonic distortion at a specific harmonic frequency with a high filtering percentage, but resonance hazards exist. Traditional damped filters offer high-pass filtering for the high-frequency range, but suffer from extra ohmic losses. C-type filters may operate in a manner similar to the tuned filters with low damping losses and marginal resonance damping capabilities. In addition, they can be designed as damped filters with increased resonance damping capability. In this paper, a methodology that facilitates sizing for the C-type damped filter parameters for harmonics mitigation and resonance damping in balanced distribution system networks is presented and discussed using the impedance-frequency index. This index evaluates the resonance damping capability provided by the damped filters analytically rather than the conventional graphical method of impedance-frequency scanning. It shows how to size shunt passive filters, while making a full use of their damping capabilities. It can disclose the parallel resonance frequencies of the equivalent system-filter impedance. A comparative study of the new approach and a conventional filter design approach, which aims to minimize total harmonic current distortion, is presented. Numerous simulation results are provided to clarify the proposed methodology, advantages, and disadvantages.