We study the energy dependence of the cross-section for exclusive photo-production of vector mesons J/Psi and its excited state Psi(2s) with the goal to find possible signs for the onset of non-linear QCD dynamics. Our study is based on two dipole models: the Golec-Biernat, Wuesthoff Model (GBW) and the Bartels, Golec-Biernat, Kowalski Model (BGK). In both models, non-linear effects are simulated through exponentiating of the leading order QCD description, where the BGK model further includes DGLAP evolution into the description. Comparing to both HERA and LHC data we find that differences between linear and non-linear implementations are relatively small at the level of photo-production cross-sections, in particular if both theoretical and experimental uncertainties are taken into account. Differences between linear and non-linear implementation are on the other hand enhanced for the ratio of ratio of Psi(2s) and J/Psi photo-production cross-sections. We find that the ratio grows with energy in the presence non-linear effects, while it remains approximately constant if non-linear effects are absent. We therefore believe that the ratio of photo-production cross-sections can provide a suitable tool to characterize the size of non-linear QCD effects at current collider energies.