Our understanding of blazars has been greatly increased in recent years by extensive multiwavelength observations, particularly in the radio, X-ray, and gamma-ray regions. Over the past decade the Whipple 10 m telescope has contributed to this with the detection of five BL Lacertae objects at very high gamma-ray energies. The combination of multiwavelength data has shown that blazars follow a well-defined sequence in terms of their broadband spectral properties. Together with providing constraints on emission models, this information has yielded a means by which potential sources of TeV emission may be identified and predictions made as to their possible gamma-ray flux. We have used the Whipple telescope to search for TeV gamma-ray emission from eight objects selected from a list of such candidates. No evidence has been found for very high energy emission from the objects in our sample, and upper limits have been derived for the mean gamma-ray flux above 390 GeV. These flux upper limits are compared with the model predictions, and the implications of our results for future observations are discussed.