An innovative strategy based on Interval Analysis (IA) is presented to the solution of inverse scattering problems. First, the inverse problem is recast to an optimization one through the definition of a suitable function to be minimized which evaluates the misfit between the measured and the reconstructed field data according to the arithmetic of intervals. Then, IA is used to check n-dimensional interval portion of the solution space and verify whether the global minimum is either present or no. The intervals which are not discarded are iteratively sub-divided and tested until suitable termination conditions are achieved. Representative results are presented and discussed to show the potentialities of Interval Analysis as applied to inverse problems in electromagnetics.