We report electron spin resonance studies of double perovskite Ba \(_2\) CoWO \(_6\) single crystals. Above \(T_\textrm{N} = 14\) K, we observe a paramagnetic resonance with \(g_\textrm{eff}\simeq 3.66\) . Upon cooling, this mode transforms into a broad antiferromagnetic resonance (AFMR) with a zero-field energy gap of about 200 GHz. The AFMR becomes barely detectable at low magnetic fields, indicating unusually strong decay processes. We argue that symmetry-allowed anisotropic spin–spin interactions are a possible reason for the pronounced spin-wave damping. Linear spin-wave theory calculations support this scenario.