The temperature dependence of the excitation spectrum in NaOsO_{3} through its metal-to-insulator transition (MIT) at 410 K has been investigated using resonant inelastic x-ray scattering at the Os L_{3} edge. High-resolution (ΔE∼56 meV) measurements show that the well-defined, low-energy magnons in the insulating state weaken and dampen upon approaching the metallic state. Concomitantly, a broad continuum of excitations develops which is well described by the magnetic fluctuations of a nearly antiferromagnetic Fermi liquid. By revealing the continuous evolution of the magnetic quasiparticle spectrum as it changes its character from itinerant to localized, our results provide unprecedented insight into the nature of the MIT in NaOsO_{3} [J. G. Vale, S. Calder, C. Donnerer, D. Pincini, Y. G. Shi, Y. Tsujimoto, K. Yamaura, M. M. Sala, J. van den Brink, A. D. Christianson, and D. F. McMorrow, Phys. Rev. B 97, 184429 (2018)PRBMDO2469-995010.1103/PhysRevB.97.184429].