Nano and micromechanical experiments allow for a fundamental understanding of how small-scale materials behave and, thus, what applications these materials can be practically applied to. For example, graphene and hexagonal boron nitride (hBN) are structurally similar. However, graphene is stronger, but hBN is tougher. This fundamental insight enables engineers to design composites balancing strength versus toughness. The more nanomaterials studied and the greater the number of methods used to study nanomechanics, the more nanomaterials are applied, likely as composites. Due to the unique properties of nanomaterials, they are strong candidates to reinforce composites in extreme applications such as high radiation environments. However, testing methods are lacking at the nano- and microscale, as manufacturing new setups is complicated and niche, and some existing testing methods have yet to be applied to nanocomposites. Many mechanical properties have yet to be directly measured at the nanoscale (e.g. high strain rate tension and out-of-plane shear of a 2D material). Nanoscale high-strain rate methods have been devised for 1D materials, but not all methods are applicable to 2D materials. In this thesis, a high strain rate tensile method is developed and validated on 1D PMMA. With this proof of concept, multilayer hBN was subjected to high strain rate tension. This validated the applicability of using a push-to-pull microdevice with a 2D material at high strain rates. This method found a strain rate sensitivity in PMMA but not in hBN. Designs for in- and out-of-plane shear devices are explored as well. Two separate material platforms were investigated to understand how 1D and 2D reinforcing nanomaterials affect the mechanical properties of composites with radiation exposure at the microscale. Those composites are carbon nanotube-reinforced silicon carbide (SiC) exposed to radiation and an hBN-reinforced covalent organic framework (COF) exposed to radiation. Pillar splitting, a simple microscale fracture toughness test, has yet to be performed on a nanomaterial-reinforced composite. Pillar splitting SiC showed the method's limitations when samples are highly defective. Nanotube reinforcement led to a weaker material likely correlated to processing more than reinforcement, while radiation increased the toughness. The hBN/COF composite showed that neutron radiation can alter the detectable bonds in the composite and strengthen, harden, and toughen the composite.