Small force measurements are needed in a large variety of cutting-edge scientific applications. However, the development of small-scale force standards and suitable calibration procedures remains challenging for national institutes of metrology. In this context, an electromagnetic force balance is under development to characterize flexible samples or calibrate force transducers down to the micronewton level. The main contribution of this work is the application to this system of a methodological proposal in order to estimate the stiffness of a f lexible cantilever. This method consists of four distinct steps based on the existing concept of equivalent representation for uncertain dynamical systems. The calculation of uncertainty for specific quantities of interest, such as stiffness, is therefore linked to this concept using interval analysis and unknown input shaping.