We discuss universal features on the electron spin resonance (ESR) of a temperature-induced Tomonaga–Luttinger liquid phase in a wide class of weakly coupled S = 1/2 antiferromagnetic spin chains such as spin ladders, spin tubes and three-dimensionally coupled spin chains. We show that the ESR linewidth of various coupled chains increases with lowering temperature while the linewidth of a single spin chain is typically proportional to temperature. This broadening with lowering temperature is attributed to anisotropic interchain interactions and has been indeed observed in several kinds of three-dimensional (3D) magnets of weakly coupled spin chains above the 3D ordering temperature. We demonstrate that our theory can account for anomalous behaviors of the linewidths in an S = 1/2 four-leg spin tube compound Cu2Cl4∙H8C4SO2 (abbreviated to Sul-Cu2Cl4) and a three-dimensionally coupled S = 1/2 spin chain compound CuCl2∙2NC5H5.