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The properties of synthetic CO emission from 3D simulations of formingmolecular clouds are studied within the SILCC-Zoom project. Since the timescales of cloud evolution and molecule formation are comparable, thesimulations include a live chemical network. Two sets of simulations with anincreasing spatial resolution (d$x=3.9$ pc to d$x=0.06$ pc) are used toinvestigate the convergence of the synthetic CO emission, which is computed bypost-processing the simulation data with the RADMC-3D radiative transfer code.To determine the excitation conditions, it is necessary to include atomichydrogen and helium alongside H$_2$, which increases the resulting CO emissionby ~7-26 per cent. 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. Anintensity-weighted average excitation temperature results in the most accurateestimate of the total CO mass. When the pixel-based excitation temperature isused to calculate the CO mass, it is over-/underestimated at low/high CO columndensities where the assumption that $^{12}$CO is optically thick while$^{13}$CO is optically thin is not valid. Further, in order to obtain aconverged total CO luminosity and hence <$X_{\rm CO}$> factor, the 3Dsimulation must have d$x\lesssim0.1$ pc. The <$X_{\rm CO}$> evolves over timeand differs for the two clouds; yet pronounced differences with numericalresolution are found. Since high column density regions with a visualextinction larger than 3~mag are not resolved for d$x\gtrsim 1$~pc, in thiscase the H$_2$ mass and CO luminosity both differ significantly from the higherresolution results and the local $X_{\rm CO}$ is subject to strong noise. Ourcalculations suggest that synthetic CO emission maps are only converged forsimulations with d$x\lesssim 0.1$ pc.

Synthetic CO emission and the $X_{\rm CO}$ factor of young molecular clouds: a convergence study