The Born cross sections of the processes e+e− → ωπ0 and e+e− → ωη are measured at center-of-mass energies between 3.773 and 4.701 GeV using a total integrated luminosity of 22.7 fb−1 collected with the BESIII detector operating at the BEPCII collider. A simple s−n dependence for the continuum process can describe the measured Born cross sections. No significant contributions from the ψ(4160), Y(4230), Y(4360), ψ(4415), Y(4660) resonances are found, which indicates relative small branching fractions for these resonances into the ωπ0 and ωη final states.