  The magnetic field of the quiet-Sun chromosphere remains a mystery for solar
physicists. The reduced number of chromospheric lines are intrinsically hard to
model and only a few of them are magnetically sensitive. In this work, we use a
3D numerical simulation of the outer layers of the solar atmosphere, to asses
the reliability of non-LTE inversions, in this case applied to the Ca II 8542
\AA\ line. We show that NLTE inversions provide realistic estimates of physical
quantities from synthetic observations.
