This paper is focused on the modeling and analysis of a pair of open complementary split ring resonators (OCSRR) for sensing purposes. Since the capacitance of the OCSRR is very sensitive to dielectric loading, it follows that the OCSRR pair is very useful for differential permittivity measurements. The proposed sensing approach is based on the measurement of the cross-mode S-parameters, particularly the cross-mode insertion loss, very sensitive to asymmetric loading. On the basis of the circuit model of the OCSRR, analytical expressions for the cross-mode insertion loss under small perturbations (asymmetries) are derived. Such expressions, of interest for sensor design, are validated through circuit and electromagnetic simulations.