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We analyse synthetic $^{12}$CO, $^{13}$CO, and [CII] emission maps ofsimulated molecular clouds of the SILCC-Zoom project, which include anon-the-fly evolution of H$_2$, CO, and C$^+$. We use simulations ofhydrodynamical and magnetohydrodynamical clouds, both with and without stellarfeedback. We introduce a novel post-processing of the C$^+$ abundance usingCLOUDY, to account for further ionization states of carbon due to stellarradiation. We report the first self-consistent synthetic emission maps of [CII]in feedback bubbles, largely devoid of emission inside them, as recently foundin observations. The C$^+$ mass is only poorly affected by stellar feedback butthe [CII] luminosity increases by $50 - 85$ per cent compared to runs withoutfeedback. Furthermore, we investigate the capability of the CO/[CII] line ratioas a tracer of the amount of H$_2$ in the clouds and their evolutionary stage.We obtain, for both $^{12}$CO and $^{13}$CO, no clear trend of the luminosityratio, $L_\mathrm{CO}/L_\mathrm{[CII]}$. It can therefore \textit{not} be usedas a reliable measure of the H$_2$ mass fraction. We note a monotonic relationbetween $L_\mathrm{CO}/L_\mathrm{[CII]}$ and the H$_2$ fraction whenconsidering the ratio for individual pixels of our synthetic maps, but withlarge scatter. Moreover, we show that assuming chemical equilibrium results inan overestimation of H$_2$ and CO masses of up to 110 and 30 per cent,respectively, and in an underestimation of H and C$^+$ masses of 65 and 7 percent, respectively. In consequence, $L_\mathrm{CO}$ would be overestimated byup to 50 per cent, and $L_\mathrm{C[II]}$ be underestimated by up to 35 percent. Hence, the assumption of chemical equilibrium in molecular cloudsimulations introduces intrinsic errors of a factor of up to $\sim2$ inchemical abundances, luminosities and luminosity ratios.

CO and [CII] line emission of molecular clouds -- the impact of stellar feedback and non-equilibrium chemistry