The search for new oxide materials with pronounced proton transport is of great importance for the fabrication of electrochemical devices capable of realizing various energy conversion processes with high efficiency. The state-of-the-art proton-conducting oxides based on Ba(Ce,Zr)O3 have been proposed as the most promising electrolytes for such devices, although they suffer from a number of drawbacks. Here, we report an in-depth analysis of the transport properties of Y-doped barium stannates as relatively new proton-conducting compounds. In detail, the single-phase BaSn1–xYxO3–δ (0 ≤ x ≤ 0.4) ceramics were successfully prepared and their electrochemical properties were analysed using a number of characterization methods, including conductivity and thermo-EMF measurements depending on oxygen partial pressure as well as electrochemical impedance spectroscopy. The data obtained clearly indicate that the Y-doping degree affects the transport properties of BaSn1–xYxO3–δ. The weakly doped stannates (0 ≤ x ≤ 0.15) are identified as pronounced n- and p-type electron conductors, while the heavily doped stannates (0.2 ≤ x ≤ 0.4) exhibit a higher ionic conductivity and a wider electrolytic domain boundary, which allows them to be considered as new potential electrolytes with good grain boundary conductivity for application in both protonic ceramic fuel and electrolysis cells.