The theory of quantum measurement of mechanical motion, describing the mutual coupling of a meter and a measured object, predicts a variety of phenomena such as quantum backaction, quantum correlations and non-classical states of motion. In spite of great experimental efforts, mostly based on nano-electromechanical systems, probing these in a laboratory setting has as yet eluded researchers. Cavity optomechanical systems, in which a high-quality optical resonator is parametrically coupled to a mechanical oscillator, hold great promise as a route towards the observation of such effects with macroscopic oscillators. Here, we present measurements on optomechanical systems exhibiting radiofrequency (62-122 MHz) mechanical modes, cooled to very low occupancy using a combination of cryogenic precooling and resolved-sideband laser cooling. The lowest achieved occupancy is n similar to 63. Optical measurements of these ultracold oscillators' motion are shown to perform in a near-ideal manner, exhibiting an imprecision-backaction product about one order of magnitude lower than the results obtained with nano-electromechanical transducers.