In this paper, we develop a reduced-order modeling technique, which is based on a low-frequency expansion of the electromagnetic field. The expansion can be written in terms of the pseudoinverse of a so-called system matrix. This pseudoinverse is given explicitly, and it is shown that it satisfies a reciprocity relation. Moreover, we show that computing matrix-vector products with this pseudoinverse essentially amounts to repeatedly solving Poisson's equation. The latter two properties allow us to efficiently compute reduced-order models via a Lanczos-type algorithm. The proposed method is illustrated by a number of numerical examples.