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This paper proposes a hybrid experimental-numerical technique, based on the boundary element method, able to reconstruct the magnetic field distribution in the free space outside the unknown field sources, without requiring the onerous process of source identification. The approach is validated by comparison with experimental data considering a Helmholtz coil system, where the connections of the coils and the supply currents can be controlled to generate different spatial distributions of the magnetic field. The presence of materials with high magnetic permeability, also involving eddy currents, is considered as well. An analysis on the reachable accuracy and on the related parameters is developed, with the final aim of obtaining a satisfactory compromise between result accuracy and experimental burden. Finally, the field values reconstructed by the proposed experimental-numerical technique are compared with the measured ones, showing a good agreement.