Improved apparatus and methods for non-invasively assessing one or more hemodynamic parameters associated with the circulatory system of a living organism. In one aspect, the invention comprises spatially compact “bracelet” embodiment adapted to accurately place and maintain a sensor (e.g., tonometric pressure sensor) with respect to the anatomy of the subject, including an optional alignment apparatus which moveably captures the sensor to, inter alia, facilitate coupling thereof to an actuator used to position the sensor during measurements. The alignment apparatus also advantageously allows the sensor position to be maintained when the fixture is removed from the subject, such as during patient transport. A completely autonomous variant of the bracelet apparatus having internal power supply and wireless interfaces is also disclosed. Methods for positioning the alignment apparatus and sensor and providing treatment to the subject are also described.