Diamond nanocrystals containing NV color centers are positioned with 100-nanometer-scale accuracy in the near-field of a high-Q SiO(2) microdisk cavity using a fiber taper. The cavity modified nanocrystal photoluminescence is studied, with Fano-like quantum interference features observed in the far-field emission spectrum. A quantum optical model of the system is proposed and fit to the measured spectra, from which the NV(-) zero phonon line coherent coupling rate to the microdisk is estimated to be 28 MHz for a nearly optimally placed nanocrystal.