A time-domain free-space extraction procedure is proposed to uniquely determine the relative complex permittivity $\epsilon _{r} (\omega)$ based on two sets of natural frequencies of the metal- and air-backed dielectric samples. A graphical analysis is applied for evaluating whether unique $\epsilon _{r} (\omega)$ can be extracted using such natural frequencies. The method is numerically validated using two dielectric samples with different $\epsilon (\omega)$ for the ideal case (no noise) and under the influence of noise with different signal-to-noise ratios (SNRs).