Rapidly rotating neutron stars are the only candidates for persistent high-frequency gravitational wave emission, for which a targeted search can be performed based on the spin period measured from electromagnetic (e.g., radio and X-ray) observations. The principal factor determining the sensitivity of such searches is the measurement precision of the physical parameters of the system. Neutron stars in X-ray binaries present additional computational demands for searches due to the uncertainty in the binary parameters. We present the results of a pilot study with the goal of improving the measurement precision of binary orbital parameters for candidate gravitational wave sources. We observed the optical counterpart of Sco X-1 in 2011 June with the William Herschel Telescope and also made use of Very Large Telescope observations in 2011 to provide an additional epoch of radial-velocity measurements to earlier measurements in 1999. From a circular orbit fit to the combined data set, we obtained an improvement of a factor of 2 in the orbital period precision and a factor of 2.5 in the epoch of inferior conjunction T 0. While the new orbital period is consistent with the previous value of Gottlieb et al., the new T 0 (and the amplitude of variation of the Bowen line velocities) exhibited a significant shift, which we attribute to variations in the emission geometry with epoch. We propagate the uncertainties on these parameters through to the expected Advanced LIGO-Virgo detector network observation epochs and quantify the improvement obtained with additional optical observations.