Scientific progress and technological advancements on novel materials are often deterred by limitations on size and quality of samples. Materials with electronic phenomena attractive for applications, and presenting many open scientific questions, are often challenging to grow. Surpassing these barriers for technological applications, or for explorations of microscopic samples, necessitates new approaches. One property important for applications and fundamental science is elasticity. The elastic tensor is defined by attractive bonds between ions and encodes the symmetries of the material, making elasticity measurements valuable for insight into the symmetries of the electronic state. Unfortunately, elasticity experiments have so far been restricted to materials that can be grown into large, clean samples. The goal of this thesis is to bridge this gap, developing a fabrication process to construct resonators directly from novel materials. This new technique uses a Focused Ion Beam (FIB) which can selectively etch or deposit with sub-µm precision. A robust workflow was developed to carve samples with length scales as small as ∌10µm into cantilevers. Because mechanical resonance modes are dependent on geometry and elastic properties, by controlling cantilever geometry, elasticity can be explored with exquisite sensitivity by measuring resonance frequencies. One promising application is the study of quantum materials, in which electronic correlations give rise to remarkable phenomena such as high-temperature (high-Tc ) superconductivity (SC). Measurements were conducted to explore electronic phenomena in the rare-earth nickelates, and the high-Tc superconductors of the cuprates and iron pnictides. This project is intended to accelerate the transition process needed to implement novel electronic materials into research and technology. The decades of materials research ordinarily spent on optimizing growth processes can be circumvented, focusing promptly on the microparticles available. The most fundamental application of this technique is elasticity studies on size and quality-limited samples. For large samples, microscale elasticity can be vastly different than macroscale elasticity. Incorporating these materials into devices relies on knowledge of their microscale elasticity. This technique is flexible and can be used for a wide range of materials and to create complex, 3D structures to explore functionality of different geometries. FIB-fabrication compared favorably to standard techniques with FIBed Si cantilevers showing deviations from literature values as low as 8% and the relative frequency resolution is superb. On cantilevers of SmFeAs(O,F) — a family that has one of the highest Tc within the iron-based superconductors — a giant anomalous softening in the elastic shear component was observed. This softening has been reported in the lower-Tc BaFe2As2 and is associated with a nematic phase, which involves the breaking of rotational symmetry via electronic interactions. This state occurs near SC, raising the question of their interplay and if they share a common origin. These measurements are the first observations of nematicity in this high-Tc family; although remarkably, the energy of the electronic-lattice coupling is weaker than in the lower-Tc families. These results show the potential of this technique in expounding upon the materials that can be studied to yield further insight into intricate electronic correlations.