This paper deals with theoretical and numerical problems related with the inverse problem of the reconstruction of the first piece of the piecewise affine approximation of the B–H nonlinear characteristic starting from the knowledge of measured flux–current relationship. The reconstruction of the first piece of the characteristic is critical, as highlighted in novel approaches reconstructing the whole characteristic without relying on the common assumption that the driving system produces a uniformly distributed magnetic field inside the specimen. In this paper a proof will be given of the uniqueness of the solution of the inverse problem based on elementary analysis arguments and a numerical procedure that, by means of the use of complementary formulations, allows one to compute and control the reconstruction error due to the numerical formulation. The paper is organized as follows: a brief discussion of the problem is reported in Section 1, the numerical formulation and the error bounds are reported in Section 2, the uniqueness of the inverse problem is addressed in Section 3 and numerical examples are reported in Section 4.