  The Born cross sections of the processes $e^+e^- \rightarrow \omega\pi^{0}$
and $e^+e^- \rightarrow \omega\eta$ 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
$\psi(4160)$, $Y(4230)$, $Y(4360)$, $\psi(4415)$, $Y(4660)$ resonances are
found, which indicates relative small branching fractions for these resonances
into the $\omega\pi^{0}$ and $\omega\eta$ final states.
