The double-differential cross sections of promptly produced J/ψ and ψ(2S) mesons are measured in pp collisions at s=7TeV, as a function of transverse momentum pT 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 4.90fb-1, respectively. The results are based on a two-dimensional analysis of the dimuon invariant mass and decay length, and extend to pT=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<pT<100GeV. These are the highest pT values for which the cross sections and ratio have been measured.