Improved apparatus and methods for non-invasively assessing one or more parameters associated with systems such as fluidic circulating systems (e.g., the circulatory system of a living organism). In a first aspect, an improved method of continuously measuring pressure from a compressible vessel is disclosed, wherein a substantially optimal level of compression for the vessel is achieved and maintained using dynamically applied dither perturbations (e.g., modulation) on the various axes associated with the vessel. In a second aspect, an improved apparatus and method are provided for monitoring hemodynamic parameters, such as blood pressure, in a continuous and non-invasive manner while operating under a single unifying scheme. One variant of this scheme using a simulated annealing (SA) type approach to determining and maintaining an optimal operating state.