In this paper the tomographic problem arising in the diagnostics of a fuel cell is discussed. This is concerned with how well the electric current density $j(r)$ be reconstructed by measuring its external magnetic field. We show that (i) exploiting the fact that the current density has to comply with Maxwell’s equations it can, in fact, be reconstructed at least up to a certain resolution, (ii) the functional connection between the resolution of the current density and the relative precision of the measurement devices can be obtained, and (iii) a procedure can be applied to determine the optimum measuring positions, essentially decreasing the number of measuring points and thus the time scale of measurable dynamical perturbations—without a loss of fine resolution. We present explicit results for (i)–(iii) by applying our formulas to a realistic case of an experimental direct methanol fuel cell.