Materials that contain soft, deformable particles exhibit a rich range of macroscopic mechanical properties. Experimental access to the mechanics at the scale of a single particle is the basis for studying and understanding the macroscopic mechanics of these materials. In this paper, we discuss experimental methods that can be used to characterize the mechanics of microscopic soft particles. We focus on the recently developed capillary micromechanics method, which yields the full linear elastic behavior of a single particle. We validate the method by comparing results for the compressive modulus to osmotic compression measurements, which provide the most direct and unambiguous measure of compressibility. We find good agreement between the two methods on a system of deformable and compressible poly-N-isopropylacrylamide microgel particles. Our results thus support the validity of the capillary micromechanics method and suggest that it could be applied to a wide range of materials that consist of deformable soft objects.