In this work, we demonstrate the preparation of easy-to-fabricate nanogranular strontium ferromolybdate/strontium molybdate core-shell ceramics and examine their properties, including tunnel magnetoresistance, magnetic field sensitivity, and temperature coefficient of the tunnel magnetoresistance. The tunnel magnetoresistance of nanogranular strontium ferromolybdate/strontium molybdate core-shell ceramics was modeled, yielding values suitable for magnetoresistive sensor applications. Such structures possess a narrow peak of magnetic flux sensibility located at about 80 mT. For magnetic flux measurement, single-domain granules with superparamagnetic behavior should be applied. The predicted TMR magnetic flux sensitivities for granules with superparamagnetic behavior amount to about 7.7% T⁻¹ and 1.5% T⁻¹ for granule sizes of 3 nm and 5 nm, respectively. A drawback of the tunnel magnetoresistance of such nanogranular core-shell ceramics is the unacceptably large value of the temperature coefficient. Acceptable values, lower than 2% K⁻¹, are obtained only at low temperatures (less than 100 K) or large magnetic flux densities (exceeding 6 T). Therefore, a Wheatstone bridge configuration should be adopted for magnetoresistive sensor design to compensate for the effect of temperature.