Using the Echellete Spectrograph Imager (ESI) on the Keck II 10 m telescope we have measured the redshifts of the host galaxies of gamma-ray bursts GRB 990506 and GRB 000418, z=1.30658+/-0.00004 and 1.1181+/-0.0001, respectively. Thanks to the excellent spectral resolution of ESI (łambda/ Δłambda=13000), we resolved the [O II] łambda3727 doublet in both cases. The measured redshift of GRB 990506 is the highest known for a dark-burst GRB, though entirely consistent with the notion that dark and non-dark bursts have a common progenitor origin. The relative strengths of the [O II], He I, [Ne III], and Hγ emission lines suggest that the host of GRB 000418 is a starburst galaxy, rather than a LINER or Seyfert 2. Since the host of GRB 000418 has been detected at submillimeter wavelengths, these spectroscopic observations suggest that the submillimeter emission is due to star formation (as opposed to AGN) activity. The [O II]-derived unobscured star formation rates are 13 and 55 M$_solar$ yr$^-1$ for the hosts of GRB 990506 and GRB 000418, respectively. In contrast, the star formation rate of the host of GRB 000418 derived from submillimeter observations is 20 times larger.