This study investigates the sensing applications of metamaterial (MTM) structures in the terahertz (THz) region and is based on a broadside-coupled diamond and square ring resonator (DSRR) structures. The resonators are designed and simulated as sensors in detail. Compared with single-sided sensors, the sensing capability of double-sided sensors provide an enhancement with respect to the sensitivity. To analyze the structure as sensor, the changes in the transmission resonance are investigated as a function of the permittivity and thickness of overlayer for the single- and double-sided MTM. The results demonstrate that this design can provide good sensitivity when sensing the chemical or biological agents that are resonant in the terahertz region of the electromagnetic spectrum. These types of designs can be employed in the many sensing applications that are of interest in the THz region.