A survey of binary systems containing pulsars was conducted, with the intention of detecting Galactic sources of very high energy γ-ray emission. Observations were carried out with the Whipple 10 m imaging atmospheric Cerenkov telescope. Standard analysis techniques were applied to these sources to search for steady, unpulsed emission. Periodic tests were also performed to search for emission correlated with both the orbital and spin phases, where appropriate. Analyses indicate that the binaries in this study do not emit detectable levels of very high energy photons within the sensitivity of our instrument. The flux upper limits presented here fail to seriously constrain emission models.