A solution to interference pumping tests in fractal fractured media of Euclidean dimension two has been developed. It is proposed in dimensioned variables with a pre-conditioning of its most sensitive parameter and a Gauss-Newton inversion. The method allows for a rapid identification of hydrodynamic parameters by fitting experimental data. The fractal dimension and the scale exponent of the hydraulic diffusion are also determined without any other calculation or reference to a theoretical medium. Thus, the results provide a reliable appraisal of how the hydrodynamic parameters evolve with the size of the system. This feature has important applications in hydrology and petroleum engineering especially when up-scaling approaches are needed.