The active galaxy Centaurus A and the X-ray binary systems Vela X-1, Centaurus X-3, and Circinus X-1 were monitored for VHE gamma-ray emission above 1 TeV with the JANZOS Cerenkov facility during 1988 and 1989. No evidence was found for persistent or episodic emission from any of these objects. Subseqeunt upper limits on the integral fluxes of 2.2 x 10(-11), 2.8 x 10(-11), 4.0 x 10(-11), and 4.2 x 10(-11) cm-2 s-1, respectively, were obtained for these objects. These limits are consistent with results of observations made by other groups.