The magnetic resonance spectra of frustrated manganite compounds La1/3Ca2/3MnO3 and BiMnO3 are calculated within the framework of orbitally dependent magnetic interactions model. The aim of the paper is an investigation of orbital structure influence and superexchange interactions’ competition effects on ferromagnetic or antiferromagnetic resonance spectra of these compounds. The description of the features of the resonance lower branches’ dependencies on the magnitude and direction of the magnetic field is proposed. It is shown that the main influence on the symmetry of dependencies is exerted by single-ion anisotropy of the Mn3+ ion, associated not only with the orbital structure, but also with the tilting distortions of oxygen octahedrons around the ions