Constraints on bulk conductivity from magnetotelluric measurements and petrological analyses of late Quaternary peridotite xenoliths from the southern Sierra Nevada allow evaluation of models commonly used to relate electrical conductivity to the physical and chemical state of the upper mantle. In these models, two conductive melts (basalt and sulfide) are embedded in a resistive matrix. Bounds on the amount of sulfide (0.06--0.4%) and the bulk conductivity (0.03--0.1 S/m) place constraints on the degree of interconnection between the melts. Because the sulfide melt is very conductive, even a small fraction of well-connected melt results in a bulk conductivity larger than 0.1 S/m. Similarly, completely disconnected melts result in bulk conductivities much less than 0.03 S/m. The only models which matched both the bulk conductivity and sulfide bounds consisted of a small fraction (<1%) interconnected basalt melt with a discontinuous sulfide phase. Such a texture is observed in laboratory experiments with much larger sulfide melt fractions, but has not been reported for small melt fractions. A variant of the Hashin-Shtrikman model and a hybrid model consisting of cascaded Hashin-Shtrikman calculations were successful in matching the magnetotelluric and petrologic constraints. With a model that appropriately simulates the melt interconnectivity, we suggest that electrical conductivity may be used to infer in situ melt properties in the mantle.