Models with warped extra dimensions offer a promising solution to the hierarchy problem. However, it is known that flavour changing neutral currents arise at tree level in models with warped extra dimensions, which can lead to fatally large corrections to rare processes in the standard model. Since the introduction of the warped mechanism in 1999 by Randall and Sundrum, modifications of the original AdS5 geometries have been considered, having different phenomenologies. In particular, it has been previously shown that CP-violation in the K-K mixing system can be suppressed in what is known as the soft-wall model, in which the extra dimension is effectively compactified via a background scalar dilation field. Prior to the work presented in this thesis, however, this study had been limited to a background geometry with a specific form. A detailed study of bosonic propagators in soft-wall models has been conducted as part of this research, yielding some novel results, which permit the study of particle interactions throughout an extended family of warped 5D backgrounds in a practicable way. This methodology has then been applied, via the development of numerical routines, to an investigation of K and B meson phenomenology in a range of geometries in this family. The relevant and necessary technical prerequisites are reviewed and discussed, including (but not limited to) some of the general properties of warped extra dimensions, the application of Kaluza-Klein theory in warped 5D, topics in flavour physics and quark mixing and the application of effective field theory methods in perturbative calculations of flavour observables. It is found that there is indeed a significant interplay between the structure of the extra dimension and flavour phenomenology at a scale of 1-10 TeV. Although it turns out that the previously studied construction was already quite well-optimised with regard to flavour constraints, it is demonstrated that one can do more to ameliorate these via deformations to the background geometry and modifications to the power law dependence of the fermion masses on the extra dimension.