Developed through the combination of two preexisting methods - a shock tube acting as an impulse heater and a flame speed measurement from a spherically expanding flame - the shock-tube flame speed method brought significant promise to enable fundamental laminar flame speed measurements at previously inaccessible temperature conditions. Nevertheless, early applications of the method, as originally devised, encountered challenges associated with flame stability and structure that limited its ability to fulfill its full potential. In this dissertation, a series of efforts undertaken to characterize and optimize the shock-tube flame speed method are reported; the newly refined methods are subsequently validated and applied to demonstrate flame speed measurements at extreme unburned-gas temperatures, up to and exceeding 1,000 K, for the first time. After introducing the fundamentals of shock tubes, spherically expanding flames, and their combination in the first-generation shock-tube flame speed method, three investigations extending the original methods are described. First, the development of a technique for performing side-wall emission imaging through a small diagnostic port allowed for the identification of axial flame distortion in shock tube experiments. Then, the side-wall imaging was again leveraged in the development of the [laser-induced] flame image velocimetry ([LI]FIV) technique as a seedless, single-point velocimetry method for combustion environments, which was used in the first systematic investigation of core-gas velocities in the post-reflected-shock environment. Finally, a meta-analysis to identify conditions producing stable flames was performed on a collection of ten groups of experiments performed using variations of the first-generation method. In the resulting binary-classifier model, the unburned-gas ratio of specific heats and the ignition location were found to most strongly affect stability, guiding the optimal selection of an oxygen-argon oxidizer mixture for future experiments and motivating the need for additional experimental flexibility. Inspired by the significant insight gained through the application of side-wall imaging to shock-tube flame experiments, and seeking to realize the flexibility required to perform optimized flame speed experiments, a novel side-wall imaging flame test section (SWIFT) was designed and procured. The SWIFT features first-of-their-kind side-wall windows designed as cemented-doublet cylindrical lenses in order to provide large field-of-view, schlieren-compatible optical access through the curved side walls of the shock tube. Together with an enhanced suite of instrumentation, the implementation of the SWIFT enabled what would become the second-generation of the shock-tube flame speed method through the studies that followed. Making use of the new schlieren capabilities, the effect of the axial position on the stability of flames was reevaluated, both using static experiments to quantify the effect of asymmetric end-wall confinement and through post-reflected-shock experiments performed near 650 K and 1 atm to observe the effect of the post-shock flow field, reaffirming the presence of significant axial distortion at a certain (6.4-cm) axial location. Then, based on the need for a model capable of extracting laminar flame data from experiments exhibiting aspherical flames, an area-averaged formulation of the linear-curvature extrapolation model (the AA-LC model) was derived for use in shock-tube flame experiments. Applied to the static and 650 K experiments at different ignition locations, the model was demonstrated to yield precise and repeatable measurements, even in cases in which flame distortion was observed. The SWIFT, side-wall schlieren, and AA-LC model were finally applied in laminar flame speed measurements of propane, norm-heptane, and iso-octane at highest-ever-reported unburned-gas temperatures, up to and exceeding 1,000 K.