  The properties of synthetic CO emission from 3D simulations of forming
molecular clouds are studied within the SILCC-Zoom project. Since the time
scales of cloud evolution and molecule formation are comparable, the
simulations include a live chemical network. Two sets of simulations with an
increasing spatial resolution (d$x=3.9$ pc to d$x=0.06$ pc) are used to
investigate the convergence of the synthetic CO emission, which is computed by
post-processing the simulation data with the \textsc{radmc-3d} radiative
transfer code. To determine the excitation conditions, it is necessary to
include atomic hydrogen and helium alongside $H_2$ and the resulting CO
emission is increased by ~20-30\%. Combining the brightness temperature of
$^{12}$CO and $^{13}$CO , we compare different methods to estimate the
excitation temperature, the optical depth of the CO line and hence, the CO
column density. An intensity-weighted average excitation temperature results in
the most accurate estimate of the total CO mass. When the pixel-based
excitation temperature is used to calculate the CO mass, it is
over-/underestimated at low/high CO column densities where the assumption that
$^{12}$CO is optically thick while $^{13}$CO is optically thin is not valid.
Further, in order to obtain a converged total CO luminosity and hence <$X_{\rm
CO}$> factor, the 3D simulation must have d$x\lesssim0.1$ pc. The <$X_{\rm
CO}$> evolves over time and differs for the two clouds; yet pronounced
differences with numerical resolution are found. Since high column density
regions with a visual extinction larger than 3~mag are not resolved for
d$x\gtrsim 1$ pc, in this case the $H_2$ mass and CO luminosity both differ
significantly from the higher resolution results and the local $X_{\rm CO}$ is
subject to strong noise. Our calculations suggest that synthetic CO emission
maps are only converged for simulations with d$x\lesssim0.1$ pc.
