We propose and demonstrate a wireless, passive, metamaterial-based sensor that allows for remotely monitoring submicron displacements over millimeter ranges. The sensor comprises a probe made of multiple nested split ring resonators (NSRRs) in a double-comb architecture coupled to an external antenna in its near-field. In operation, the sensor detects displacement of a structure onto which the NSRR probe is attached by telemetrically tracking the shift in its local frequency peaks. Owing to the NSRR's near-field excitation response, which is highly sensitive to the displaced comb-teeth over a wide separation, the wireless sensing system exhibits a relatively high resolution (<1 mu m) and a large dynamic range (over 7 mm), along with high levels of linearity (R-2 > 0.99 over 5 mm) and sensitivity (>12.7 MHz/mm in the 1-3 mm range). The sensor is also shown to be working in the linear region in a scenario where it is attached to a standard structural reinforcing bar. Because of its wireless and passive nature, together with its low cost, the proposed system enabled by the metamaterial probes holds a great promise for applications in remote structural health monitoring.