Based on 14.7 fb-1 of e+e- annihilation data collected with the BESIII detector at the BEPCII collider at 17 different center-of-mass energies between 3.7730 GeV and 4.5995 GeV, Born cross sections of the two processes e+e-→pp¯η and e+e-→pp¯ω are measured for the first time. No indication of resonant production through a vector state V is observed, and upper limits on the Born cross sections of e+e-→V→pp¯η and e+e-→V→pp¯ω at the 90% confidence level are calculated for a large parameter space in resonance masses and widths. For the current world average parameters of the ψ(4230) of m=4.2187 GeV/c2 and Γ=44 MeV, we find upper limits on resonant production of the pp¯η and pp¯ω final states of 7.5 pb and 10.4 pb at the 90% CL, respectively