The double-differential cross sections of promptly produced J/ψ and ψ(2S) mesons are measured in pp collisions at sqrt[s]=7 TeV, as a function of transverse momentum p_{T} and absolute rapidity |y|. The analysis uses J/ψ and ψ(2S) dimuon samples collected by the CMS experiment, corresponding to integrated luminosities of 4.55 and 4.90 fb^{-1}, respectively. The results are based on a two-dimensional analysis of the dimuon invariant mass and decay length, and extend to p_{T}=120 and 100 GeV for the J/ψ and ψ(2S), respectively, when integrated over the interval |y|<1.2. The ratio of the ψ(2S) to J/ψ cross sections is also reported for |y|<1.2, over the range 10<p_{T}<100 GeV. These are the highest p_{T} values for which the cross sections and ratio have been measured.