We develop a prescription for estimating the interstellar medium oxygen abundances of distant star-forming galaxies using the ratio EWR_{23} formed from the equivalent widths of the [O II] 3727, [O III] 4959,5007 and Hbeta nebular emission lines. This EWR_{23} approach essentially identical to the widely-used R_{23} method of Pagel etal (1979). Using data from three spectroscopic surveys of nearby galaxies, we conclude that the emission line equivalent width ratios are a good substitute for emission line flux ratios in galaxies with active star formation. The RMS dispersion between EWR_{23} and the reddening-corrected R_{23} values is sigma(log R_{23})leq0.08 dex. This dispersion is comparable to the emission-line measurement uncertainties for distant galaxies in many spectroscopic galaxy surveys, and is somewhat smaller than the uncertainties of sigma(O/H)~0.15 dex inherent in strong-line metallicity calibrations. Because equivalent width ratios are partially insensitive to interstellar reddening effects, emission line equivalent width ratios should be superior to flux ratios when reddening corrections are not available. The EWR_{23} method presented here is likely to be most useful for statistically estimating the mean metallicities for large samples of galaxies to trace their chemical properties as a function of redshift or environment. The approach developed here is used in a companion paper (Kobulnicky etal 2003) to measure the metallicities of star-forming galaxies at z=0.2 - 0.8 in the Deep Extragalactic Evolutionary Probe spectroscopic survey of the Groth Strip.