The characteristics of biochemical sensors based on photonic crystal (PC) resonators are investigated in this work. The PC structure consists of holes arranged in a hexagonal lattice on a silicon slab. The nanoring resonator is formed by removing certain holes along a hexagonal trace. The hexagonal nanoring resonator is sandwiched by two PC waveguides that are formed by removing two lines of holes. The trapping of biomolecules, e.g., DNAs or proteins, in a functionalized sensing hole introduces a shift in resonant wavelength peak in the output terminal. We demonstrate two resonator designs: single and dual nanorings. The quality factor of the single nanoring resonator is 2400. The dual nanoring resonator reveals two different resonant modes. The propagated directions of dropped light for these two modes are antiparallel. The quality factors for these two resonant modes are 2100 and 1855, respectively. This dual nanoring resonator has a novel sensing mechanism, making it capable of simultaneously sensing two different biomolecules.