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 an apparatus adapted to automatically and accurately place and maintain a sensor (e.g., tonometric pressure sensor) with respect to the anatomy of the subject. The apparatus comprised of a sensor device removably coupled to an actuator which is used to position the sensor during measurements. Methods for positioning the alignment apparatus and sensor, and operating the apparatus, are also disclosed.