We present results from follow-up observations of a sample of 80 radio sources, originally detected as part of the 15.2-GHz Ninth Cambridge (9C) survey. The observations were carried out, close to simultaneously, at two frequencies: 15.7GHz, using the Arcminute Microkelvin Imager (AMI) Large Array, and 93.2GHz, using the Combined Array for Research in Millimeter-wave Astronomy (CARMA). There is currently little direct information on the 90-GHz-band source count for S<~1Jy. However, we have used the measured 15.7-to-93.2-GHz spectral-index distribution and 9C source count to predict the differential source count at 93.2GHz as 26+/-4(S/Jy)^-2.15^Jy^-1^sr^-1^; our projection is estimated to be most accurate for 10<~S<~100mJy. Our estimated differential count is more than twice the 90-GHz prediction made by Waldram et al. (2007, Cat. J/MNRAS/379/1442); we believe that this discrepancy is because the measured 43-GHz flux densities used in making their prediction were too low. Similarly, our prediction is significantly higher than that of Sadler et al. (2008, Cat. J/MNRAS/385/1656) at 95GHz. Since our spectral-index distribution is similar to the 20-to-95-GHz distribution measured by Sadler et al. and used in making their prediction, we believe that the difference is almost entirely attributable to the dissimilarity in the lower frequency counts used in making the estimates.