The granular structure and the dielectric characteristics of the ceramic (Ba0.5Sr0.5)Nb2O6 solid solution are studied. The ceramic is found to be characterized by a homogeneous, dense, almost pore-free microstructure consisting of crystallites 5–10 µm in size. At room temperature, (Ba0.5Sr0.5)Nb2O6 exhibits elongated hysteresis loops. The ceramic undergoes a diffuse phase transition from a paraelectric state into the state of relaxor ferroelectric in the temperature range T = 340–385 K upon cooling. Scaling is shown to weakly change the ceramic characteristics of the material.