Stroke identification by means of microwave tomography requires a very accurate reconstruction of the dielectric properties inside patient’s head. This is possible when a precise measurement system is combined with a full nonlinear inversion method. In this article, the inversion of S-parameter data collected in a metallic chamber is performed with a nonlinear inversion strategy in Lebesgue spaces with nonconstant exponents. This is the first time that this kind of nonlinear S-parameter electromagnetic formulation has been applied to this problem. The inverse-scattering method incorporates a 2-D electromagnetic model of the imaging chamber based on a finite-element formulation, which has led to a complete redefinition of the solving procedure with respect to previous works. This allows a suitable description of the multistatic S-parameters due to the interactions between the incident radiation and the structure under test. The developed inversion procedure is first assessed by means of numerical simulations. The experimental results, obtained with a clinical microwave system prototype containing a liquid-filled 3-D SAM phantom with an inhomogeneity mimicking a hemorrhagic stroke, further prove the effectiveness of the proposed approach.