We present measurements of the Born cross sections for the processes e+e-→ωχc1 and ωχc2 at center-of-mass energies s from 4.308 to 4.951 GeV. The measurements are performed with data samples corresponding to an integrated luminosity of 11.0 fb-1 collected with the BESIII detector operating at the Beijing Electron Positron Collider storage ring. Assuming the e+e-→ωχc2 signals come from a single resonance, the mass and width are determined to be M=(4413.6±9.0±0.8) MeV/c2 and Γ=(110.5±15.0±2.9) MeV, respectively, which is consistent with the parameters of the well-established resonance ψ(4415). In addition, we also use one single resonance to describe the e+e-→ωχc1 line shape and determine the mass and width to be M=(4544.2±18.7±1.7) MeV/c2 and Γ=(116.1±33.5±1.7) MeV, respectively. The structure of this line shape, observed for the first time, requires further understanding.