The LHC is expected to fid new physics beyond the Standard Model (BSM). Technicolor models are a class of BSM models which involve a new strongly interacting sector responsible for electroweak symmetry breaking (EWSB). The phenomenological viability of these models depends on features such as the existence of an infrared fixed point (IRFP) at strong coupling, and the size of the mass anomalous dimension at this fixed point. As these features are at strong coupling they are not accessible to perturbative methods, and so need to be investigated non-perturbatively using lattice methods. In this thesis, two candidate Technicolor theories are investigated using two independent and complementary lattice methods, the Schrodinger Functional (SF) and the Monte Carlo Renormalisation Group (MCRG), to measure the running of the coupling and the anomalous mass dimension in these theories.