A numerical approach is proposed that aims to detect, by means of interrogating microwaves, the locations, shapes, and dielectric properties of unknown bodies inside an investigation volume. The integral vector equation of electromagnetic scattering is numerically inverted by the moment method in terms of the distribution of the equivalent electric current density vector for localization purposes; then, after using a suitable iterative procedure, the shaping process is performed. The dielectric properties of the localized and shaped bodies are obtained by relating the equivalent current density vector to the total electric field calculated inside them. The theoretical possibilities and limitations are considered regarding the use of the map of the distribution of such an equivalent current density to model a three-dimensional scene. Some numerical simulations are performed and the preliminary results show the capabilities of the proposed method (even when measurement errors and noise are taken into account) in a dielectric range for which the Born approximation does not hold.