X- and Q-band electron paramagnetic resonance studies have been carried out on a polycrystalline superconductor YBa_1.9Na_0.1Cu₃O_{7- delta} (Y-Ba-Na-Cu-O) over the temperature range 4.2-300 K. It is concluded that the monovalent Na⁺ ions substitute for Ba²⁺ ions, and not for Cu²⁺ ions. The onset of the superconducting transition is determined to occur at 91 K, while the absorption of microwaves in low magnetic fields begins to occur below 100 K. The value of the upper critical field estimated here, as well as that of the specific heat coefficient are lower than those reported for the pure YBa₂Cu₃O_{7- delta} ceramic. The local symmetry about the Cu²⁺ ion in the phase of the sample with increased oxygen vacancy content, responsible for the Cu²⁺ EPR signal, is deduced to be orthorhombic over the entire range of temperature investigated, as revealed by the Cu²⁺ principal values (g_z, g_x and g_y), which are, in turn, used to estimate the energy-level sequence for the Cu²⁺ ion. The covalency effect due to Cu-O bonding is found to be significant. The hyperfined splitting constant mod A_z mod , as estimated from the weak hyperfine structure at low magnetic fields, is estimated to be 8 mT at 4.2 K. The sample exhibits magnetic memory in the superconducting state.