  Electromagneto-quasistatic (EMQS) field formulations are often dubbed as
Darwin-type field formulations which approximate the Maxwell equations by
neglecting radiation effects while modelling resistive, capacitive, and
inductive effects. A common feature of EMQS field models is the Darwin-Amp\'ere
equation formulated with the magnetic vector potential and the electric scalar
potential. EMQS field formulations yield different approximations to the
Maxwell equations by choice of additional gauge equations. These EMQS
formulations are analyzed within the port-Hamiltonian system (PHS) framework.
It is shown via the PHS compatibility equation that formulations based on the
combination of the Darwin-Amp\'ere equation and the full Maxwell continuity
equation yield port-Hamiltonian systems implying numerical stability and
specific EMQS energy conservation.
