Lithium metal solid-state batteries (LiSSBs) present new challenges in the measurement of material, component, and cell mechanical behaviors and in the measurement and theory of fundamental mechanical-electrochemical (thermodynamics, transport, and kinetics) couplings. Here, we classify the major mechanical and electrochemical-mechanical (ECM) studies underway and provide an overview of major mechanical testing platforms. We emphasize key distinctions among testing platforms, including tip- vs. platen-based sample compression, surface- vs. volume-based analysis, ease of integration with a vacuum or inert atmosphere environment, the ability to control and measure force/displacement over long periods of time, ranges of force and contact area, and others. Among the techniques we review, nanoindentation platforms offer some unique benefits associated with being able to use both tip-based nanoindentation techniques as well as platen-based compression over areas approaching 1 mm2. Sample design is also important: while most efforts are particle-based (i.e., using particles of solid electrolyte and cathode-active materials and densifying them using sintering or pressure), the resulting electrochemical response is from the overall collection of particles present. In contrast, thin-film (<1 μm) solid-state battery materials (e.g., Li, LiPON, LCO) provide well defined and uniform structures well suited for fundamental electrochemical-mechanical studies and offer an important opportunity to drive underlying scientific advances in LiSSB and other areas. We believe there are exciting opportunities to advance the measurement of both mechanical properties and electrochemical-mechanical couplings through the careful and novel co-design of test structures and experimental approaches for LiSSB materials, components, and cells.