A method and apparatus for determining the mean arterial blood pressure (MAP) of a subject during tonometric conditions. In one embodiment, the apparatus comprises one or more pressure and ultrasound transducers placed over the radial artery of a human subject's wrist, the latter transmitting and receiving acoustic energy so as to permit the measurement of blood velocity during periods of variable compression of the artery. During compression, the ultrasound velocity waveforms are recorded and processed using time-frequency analysis. The time at which the mean time-frequency distribution is maximal corresponds to the time at which the transmural pressure equals zero, and the mean pressure read by the transducer equals the mean pressure within the artery. In another aspect of the invention, the ultrasound transducer is used to position the transducer over the artery such that the accuracy of the measurement is maximized. In yet another aspect of the invention, a wrist brace useful for measuring blood pressure using the aforementioned apparatus is disclosed. A method of continuously estimating systolic and diastolic pressure is also described.