Recently, Jones et al. (1997) used the Ryle telescope, operating at a frequency of 15 GHz, to detect a flux decrement in the direction of the quasar pair PC1643+461A,B. They interpreted this signal as the Sunyaev-Zel'dovich effect (SZE) produced by a distant cluster of galaxies. In the course of an effort to measure CMB anisotropies using the VLA at 8.4 GHz, Richards et al. (1997) detected a similar, but smaller, decrement which we refer to as VLA1312+4237. They also proposed that this signal might be explained as the SZE signal of a distant galaxy cluster. We report observations in the direction of these claimed sources with the Berkeley Illinois Maryland Association (BIMA) interferometer operating at 28.5 GHz. We find no evidence for SZE emission in the direction of either of the claimed sources. In the case of PC1643+4631, the BIMA data are inconsistent with the cluster emission model proposed by Jones et al. (1997) at greater than 99.99% confidence. Together with published x-ray and optical searches, these results make a compelling case against the existence of a massive cluster in the direction of PC1643+4631. Because of the different scales to which the VLA and BIMA instruments are sensitive, the BIMA observations are not as constraining for the VLA1312+4237 source. The BIMA data are inconsistent with the cluster model proposed by Richards et al. (1997) at approximately 80% confidence.