According to the scaling laws for nanomechanical resonators, many of their metrological properties improve when downscaled. This fact encourages for constant miniaturization of MEMS/NEMS based sensors. It is a well known fact, that the laws of classical physics cannot be used to describe the systems which are arbitrarily small. In consequence, the classical description of nanoresonators must break down for sufficiently small and cool systems and then the quantum effects cannot be neglected. One of the fundamental question which arises is, how one may investigate quantum effects in MEMS/NEMS sensors and what is the influence of quantum effects on the performance of such systems. In this paper we would like to raise those issues by presenting the results of our work related to our estimations and calculations of MEMS/NEMS dynamics. The first and second sections are of theoretical character. In the first section (Classical modeling), we describe the classical methods for describing the resonator dynamics and the classical limit on the resolution of MEMS/NEMS based force sensors, which is set by the thermomechanical noise. In the second section (Quantum aspects), we concentrate on the quantum description of micro and nanoresonators and the influence of quantum effects, such as zero-point motion and back-action, on their performance (quantum limits). The third section is devoted to the presentation of our experimental methods of MEMS/NEMS deflection metrology, i.e. Optical Beam Deflection method (OBD) and fibre optics interferometry.