Born cross sections for the processes e(+)e(-) -> omega eta and e(+)e(-) -> omega pi(0) have been determined for centerof-mass energies between 2.00 and 3.08GeVwith the BESIII detector at the BEPCII collider. The results obtained in this work are consistent with previous measurements but with improved precision. Two resonant structures are observed. In the e(+)e(-) -> omega eta cross sections, a resonance with a mass of (2176 +/- 24 +/- 3) MeV/c(2) and a width of (89 +/- 50 +/- 5) MeV is observed with a significance of 6.2 sigma. Its properties are consistent with the phi(2170). In the e(+)e(-) -> omega pi(0) cross sections, a resonance denoted Y (2040) is observed with a significance of more than 10 sigma. Its mass and width are determined to be (2034 +/- 13 +/- 9) MeV/c(2) and (234 +/- 30 +/- 25) MeV, respectively, where the first uncertainties are statistical and the second ones are systematic. (C) 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license.