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Transiting planets around bright stars have allowed the detailed follow-up and characterization of exoplanets, such as the study of exoplanetary atmospheres. The Transit Ephemeris Refinement and Monitoring Survey is refining the orbits of the known exoplanets to confirm or rule out both transit signatures and the presence of additional companions. Here we present results for the companion orbiting HD 114762 in an eccentric 84 day orbit. Radial velocity analysis performed on 19 years of Lick Observatory data constrain the uncertainty in the predicted time of mid-transit to ∼5 hr, which is less than the predicted one-half day transit duration. We find no evidence of additional companions in this system. New photometric observations with one of our Automated Photoelectric Telescopes at Fairborn Observatory taken during a revised transit time for companion b, along with 23 years of nightly automated observations, allow us to rule out on-time central transits to a limit of ∼0.001 mag. Early or late central transits are ruled out to a limit of ∼0.002 mag, and transits with half the duration of a central transit are ruled out to a limit of ∼0.003 mag.