Abstract The acoustic characterization of porous materials with rigid solid frame plays a key role in the prediction of the acoustic behavior of any dynamic system that incorporates them. In order to obtain an accurate prediction of its frequency-dependent response, a suitable choice of the parametric models for each material is essential. However, such models could be inadequate for a given material or only valid in a specific frequency range. In this work, a novel non-parametric methodology is proposed for the characterization of the acoustic properties of rigid porous materials. Unlike most widespread methodologies, this technique is based on the solution of a sequence of frequency-by-frequency well-posed inverse problems, thus increasing the characterization accuracy. Once a reduced number of experimental measurements is available, the proposed method avoids the a priori choice of a parametric model.