Limited sensitivity and sensing range are arguably the greatest challenges in\nmicrowave sensor design. Recent attempts to improve these properties have\nrelied on metamaterial- (MTM-) inspired open-loop resonators (OLRs) coupled to\ntransmission lines (TLs). Although the strongly resonant properties of the OLR\nsensitively reflect small changes in the environment through a shift in its\nresonance frequency, the resulting sensitivities remain ultimately limited by\nthe level of coupling between the OLR and the TL. This work introduces a novel\nsolution to this problem that employs negative-refractiveindex TL (NRI-TL) MTMs\nto substantially improve this coupling so as to fully exploit its resonant\nproperties. A MTM-infused planar microwave sensor is designed for operation at\n2.5 GHz, and is shown to exhibit a significant improvement in sensitivity and\nlinearity. A rigorous signal-flow analysis (SFA) of the sensor is proposed and\nshown to provide a fully analytical description of all salient features of both\nthe conventional and MTM-infused sensors. Full-wave simulations confirm the\nanalytical predictions, and all data demonstrate excellent agreement with\nmeasurements of a fabricated prototype. The proposed device is shown to be\nespecially useful in the characterization of commonly-available\nhigh-permittivity liquids as well as in sensitively distinguishing\nconcentrations of ethanol/methanol in water.\n