The low-field magnetoresistance properties in double-perovskite strontium ferromolybdate core–shell structures arise from spin-dependent tunneling through a barrier formed by the shell. It is strongly dependent on synthesis conditions. In this work, first, the resistivity behavior of granular strontium ferromolybdate ceramics comprising intergrain tunnel barriers is reviewed. Based on this generalization, the modification of the tunneling process with barrier thickness and interface conditions is demonstrated. For the first time, equations for the magnetoresistance in each special case are derived.