We consider the solution, using boundary elements (BEs), of the surface integral equation (SIE) system arising in electromagnetic testing of conducting bodies, with an emphasis on situations, such that $o(1) \leq ({\omega \varepsilon _{0}/\sigma })^{1/2} \leq O(1)$ and $L ({\omega \sigma \mu _{0}})^{1/2} = O(1)$ , which includes in particular the case of eddy current (EC) testing and assuming $L\omega ({\varepsilon _{0} \mu _{0}})^{1/2} \leq 2\pi $ , i.e., low-frequency conditions ( $L$ : diameter of conducting body). Earlier approaches for dielectric objects at low frequencies are not applicable in the present context. After showing that a simple normalization of the BE system significantly improves its conditioning, we propose a multi-step solution method based on block-successive over-relaxation iterations, which facilitates the use of direct solvers and converges within a few iterations for the considered range of physical parameters. This new treatment, albeit simple, allows to perform EC-type analyses using standard Maxwell SIE formulations, avoiding the adverse consequences of ill-conditioning for low frequencies and high conductivities. Its performance and limitations are studied on three numerical examples involving low frequencies and high conductivities.