Finding new materials with antiferromagnetic (AFM) Kitaev interaction is an urgent issue for quantum magnetism research [1]. In this work, we conclude that Na₃Co₂SbO₆ and Na₂Co₂TeO₆ are new honeycomb cobalt-based systems with AFM Kitaev interaction by carrying out inelastic neutron scattering experiments and subsequent analysis [1]. The spin-orbit excitons observed at 20-28 meV in both compounds strongly support the idea that Co²⁺ ions of both compounds have a spin-orbital entangled J_eff=1/2 state. Furthermore, we found that a generalized Kitaev-Heisenberg Hamiltonian can describe the spin-wave excitations of both compounds with additional 3^rd nearest-neighbor interaction. Our best-fit parameters show significant AFM Kitaev terms and off-diagonal symmetric anisotropy terms of a similar magnitude in both compounds. We also found a strong magnon-damping effect at the higher energy part of the spin waves, entirely consistent with observations in other Kitaev magnets. Our work suggests Na₃Co₂SbO₆ and Na₂Co₂TeO₆ as rare examples of the AFM Kitaev magnets based on the systematic studies of the spin waves and analysis.