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 application. Such structures possess a narrow peak of magnetic flux sensibility located at about 125 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 % per T and 1.5 % per T for granules sizes of 6.8 nm and 4 nm, respectively. A drawback of the tunnel magnetoresistance of such nanogranular core-shell ceramics is the unacceptable large value of the temperature coefficient. Acceptable values, lower than 2 % per K, 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 sensors design to compensate the effect of temperature.