Diagnosing the temperatures and densities of plasmas is critical to the understanding of a wide variety of phenomena. Everything from equations of state for warm dense matter (WDM) found in Jovian planets and inertial confinement fusion (ICF) to turbulent and dissipative processes in laser-produced plasmas, rely on accurate and precise measurements of temperature and density. This work presents improvements on two distinct techniques for measuring temperatures and densities in plasmas: x-ray Thomson scattering (XRTS), and Langmuir probes (LPs). At the OMEGA laser facility, experiments on warm dense matter were performed by firing lasers at an ablator foil and driving a planar shock into cryogenically cooled liquid deuterium. XRTS in the collective scattering regime was implemented to probe the matter, measuring densities of n_e ~ 4.3 x 10²³ cm^-3, temperatures of T_e ~ 12 eV and ionizations of Z ~ 1.0. Through an extension to XRTS theory for inhomogeneous systems, it was possible to extract an additional parameter, the length scale of the shock, whose value of ? ~ 1.33 nm was consistent with the predicted mean free path, and therefore the thickness of the shock. A unique triple Langmuir probe prototype was designed and tested at the Gregori group's lab at the University of Oxford. This probe was designed for a high temporal resolution of ~ 200 MHz for probing laser-produced shocks. The probes were used to measure the shock formed from ablating carbon rods in an argon gas fill. The probe yielded plasma parameters of n_e ~ 1.0 x 10¹⁷ cm^-3 , and T^e ~ 1.5 eV, consistent with measurements from interferometry and emission spectroscopy.