A photonic crystal nanocavity with a Quality (Q) factor of 1.4 x 10(6), a mode volume of 0.78(lambda/n)(3), and an operating wavelength of 637 nm is designed in a silicon nitride (SiN(x)) ridge waveguide with refractive index of 2.0. The effect on the cavity Q factor and mode volume of single diamond nanocrystals of various sizes and locations embedded in the center and on top of the nanocavity is simulated, demonstrating that Q > 1 x 10(6) is achievable for realistic parameters. An analysis of the figures of merit for cavity quantum electrodynamics reveals that strong coupling between an embedded diamond nitrogen-vacancy center and the cavity mode is achievable for a range of cavity dimensions.