This work is a contribution to the understanding of the electrical resistivity in strontium ferromolybdate (Sr2FeMoO6-δ, SFMO) ceramics. It demonstrates that an appropriate thermal treatment leads to the formation of dielectric SrMoO4 shells at the surface of SFMO nanograins. In samples without SrMoO4 shells, the sign of the temperature coefficient of resistance changes with increasing temperature from negative at very low temperatures to positive at higher temperatures. Samples exhibiting a negative temperature coefficient contain SrMoO4 shells and demonstrate a behavior of the resistivity that can be described in terms of the fluctuation-induced tunneling model, and near room temperature the conductivity mechanism converts to a variable-range hopping one. The results of this work serve as a starting point for the understanding of the low-field magnetoresistance which is very promising for spintronic device application.