  We study a~quasilinear coupled magneto-quasistatic model from a~systems
theoretic perspective.} First, by taking the injected voltages as input and the
associated currents as output, we prove that the magneto-quasistatic system is
passive. Moreover, by defining suitable Dirac and resistive structures, we show
that it admits a~representation as a~port-Hamiltonian system. Thereafter, we
consider dependence on initial and input data. We show that the current and the
magnetic vector potential can be estimated by means of the initial magnetic
vector potential and the voltage. We also analyse the free dynamics of the
system and study the asymptotic behavior of the solutions for $t\to\infty$.
