  Magnetic fields are predicted to have a crucial impact on the structure,
evolution and chemistry of protoplanetary disks. However, a direct detection of
the magnetic field towards these objects has yet to be achieved. In order to
characterize protoplanetary disk magnetic fields, we investigate the impact of
the Zeeman effect on the (polarized) radiative transfer of emission from
paramagnetic molecules excited in protoplanetary disks. While the effects of
the Zeeman effect are commonly studied in the circular polarization of spectral
lines, we perform a comprehensive modeling also of the Zeeman-induced
broadening of spectral lines and their linear polarization. We develop
simplified radiative transfer models adapted to protoplanetary disks, which we
compare to full three-dimensional polarized radiative transfer simulations. We
find that the radiative transfer of circular polarization is heavily affected
by the expected polarity-change of the magnetic field between opposite sides of
the disk. In contrast, Zeeman broadening and linear polarization are relatively
unaffected by this sign change due to their quadratic dependence on the
magnetic field. We can match our simplified radiative transfer models to full
polarization modeling with high fidelity, which in turn allows us to prescribe
straight-forward methods to extract magnetic field information from Zeeman
broadening and linear polarization observations. We find that Zeeman broadening
and linear polarization observations are highly advantageous methods to
characterize protoplanetary disk magnetic fields as they are both sensitive
probes of the magnetic field and are marginally affected by any sign change of
the disk magnetic field. Applying our results to existing circular polarization
observations of protoplanetary disk spectral lines suggests that the current
upper limits on the toroidal magnetic field strengths have to be raised.
