I shall first give a brief review of some techniques we have developed to derive novel perturbation formulas for (fixed frequency) electromagnetic fields in the presence of small inhomogeneities. Secondly I shall demonstrate how these formulas may be used to give very accurate approximations to the volume and the location of the inhomogeneities, based on fairly simple electromagnetic boundary measurements. Finally, time permitting, I shall discuss the validity (and possible extensions) of our formulas to high (and variable) frequency situations.