We present a study of high-resolution long-slit spectra of the narrow-line regions (NLR) of NGC 1068 and NGC 4151 obtained with the Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope (HST). Five orbits of HST time were used to obtained spectra at five parallel slit configurations, at position angle of 58 degrees, across the NLR of NGC 4151. Six parallel slit configurations at position angle 38 degrees were obtained across the NLR of NGC 1068. Spectra were dispersed with the medium resolution G430M grating at resolving power about 9000 which gave radial velocity measurements accurate to 30 km/s. The spectra have a spatial resolution of 0.2 arcseconds across and 0.1 arcseconds along each slit. The narrow bandpass filter allowed transmission of the two forbidden oxygen lines, 4959 and 5007 angstrom, which we used to measure the redshift of each bright kinematic component. Biconical outflow models were generated to match the data and for comparison to previous models developed with lower dispersion observations. Radio maps of the NLR were obtained for both galaxies and were used to examine the dependency of the NLR cloud velocities on the radio structure. The kinematics of the NLR appeared to be unaffected by the radio jet in both cases.