Spontaneous fluctuations are a robust phenomenon of plasmas near equilibrium, which does not depend on the existence of instabilities, and their characterization provides valuable information about the role of the relativistic temperatures $T∼ mc^2$ in relativistic regimes. In this paper, we study the broadband spontaneous electromagnetic fluctuations in a relativistic and magnetized pair plasma described by Maxwell–Jüttner distribution functions, based on the fluctuation-dissipation theorem and particle-in-cell simulations. It is shown that the transverse electromagnetic fluctuations are constrained by a temperature-independent critical frequency $ømega _m̊c=sqrt̊Ømega _rc̊^2+(ck)^2$, which separates the collisionless damping regime ($| ømega | łt ømega _rm̊$) from the case where the waves can propagate without damping ($| ømega | gt ømega _rm̊$). Further, relativistic simulations show an excellent agreement between analytical and numerical results. We expect this formalism to contribute to obtaining useful physical information about the state of relativistic plasmas.