Characterizing the mechanical response of common nanoscale contact geometries is vitally important to fields such as microelectromechanical systems (MEMS) where the behavior of nanoscale contacts can in large part determine system reliability and lifetime. Therefore a research program was undertaken that focused on the development of innovative nanoindentation-based techniques capable of quantifying the mechanical response of freestanding nanostructures. Nanoindentation was used since it is a non-destructive, high resolution technique that has been proven to be very useful in characterizing materials at the nanoscale. Examples of tested structures include single crystalline nanoparticles and polycrystalline nanoposts. From these experiments methods to characterize the structures' effective elastic modulus, flow stress, fracture toughness and activation volume required for plasticity have been developed. It was noted that both modulus and toughness in nanoparticles scale with average contact stress. This result has lead to the development of an experimental analysis technique that accounts for the hydrostatic component of pressure which develops in a material under contact. The effect of hydrostatic pressure on indentation modulus is currently not accounted for in nanoindentation even though it is shown to be important at length scales below 100 nm.