The production of omega-mesons in the pp->pp omega reaction has been investigated with the COSY-ANKE spectrometer for excess energies of 60 and 92MeV by detecting the two final protons and reconstructing their missing mass. The large multipion background was subtracted using an event-by-event transformation of the proton momenta between the two energies. Differential distributions and total cross sections were obtained after careful studies of possible systematic uncertainties in the overall ANKE acceptance. The results are compared with the predictions of theoretical models. Combined with data on the phi-meson, a more refined estimate is made of the Okubo-Zweig-Iizuka rule violation in the phi/omega production ratio.