We compare an inverse problem approach to parameter estimation with homogenization techniques for characterizing the electrical response of composite dielectric materials in the time domain. We first consider an homogenization method, based on the periodic unfolding method, to identify the dielectric response of a complex material with heterogeneous micro-structures which are described by spatially periodic parameters. We also consider electromagnetic interrogation problems for complex materials assuming multiple polarization mechanisms with distributions of parameters. An inverse problem formulation is devised to determine effective polarization parameters specific to the interrogation problem. We compare the results of these two approaches with the classical Maxwell-Garnett mixing model and a simplified model with a weighted average of parameters. Numerical results are presented for a specific example involving a mixture of ethanol and water (modeled with multiple Debye mechanisms). A comparison between each approach is made in the frequency domain (e.g., Cole-Cole diagrams), as well as in the time domain (e.g., plots of susceptibility kernels).