A series of new wholly aromatic (co)polyesters based onm-substituted bifunctional comonomers—4′-hydroxybiphenyl-3-carboxylic (3HBCA) and 3-hydroxybenzoic (3HBA) acids with molar ratios of 3HBCA:3HBA from 0:100 to 60:40, respectively—was synthesized. NMR and FTIR spectroscopy methods proved the full compliance of the copolymer composition with the target ratio of comonomers, as well as high compositional homogeneity (absence of block sequences). The resulting copolyesters have a sufficiently high molecular weight and their intrinsic viscosity values are in the range of 0.6–0.8 dL/g. Thermal analysis showed that all 3HBCA-3HBA copolyesters are amorphous, and with an increase in the content of biphenyl units (3HBCA), the glass transition temperature increases significantly (up to 190 °C). The onset of the intense thermal decomposition of the synthesized polyesters occurs above 450 °C. Thus, this indicates a sufficiently high thermal stability of these polyesters. Rheological measurements have shown that melts of copolyesters with a high content of 3HBCA units exhibit anisotropic properties. At the same time, the method of polarization optical microscopy did not confirm the transition to the liquid crystal state for these polyesters. These results confirm that it is possible to obtain high-performance polyesters based on 3HBCA, but not a mesogenic comonomer. Thus, 3HBCA is a promising comonomer for the synthesis of new thermotropic copolyesters with controlled anisotropic properties.