A method for determination of the location, shape, and material properties of a 3D object from measurements of the scattered field, when the object is successively illuminated by a number of incident fields is presented. This work extends the method previously developed for reconstructions of 2D permittivity and conductivity from electromagnetic measurements to the more complicated full-vector 3D electromagnetic inversion. Furthermore, a frequency hopping strategy to improve the resolution of the unknown objects when the frequency is raised, is underlined. Results of numerical experiments are presented to illustrate both strengths and weaknesses of the method.