In this thesis, we consider techniques to characterise a Solar System test for modified gravity theories with an inherent preferred acceleration scale (reducing to MOdified Newtonian Dynamics (MOND) in its non-relativistic limit). We further explore the use of measurements from the forthcoming LISA Pathfinder mission to test these theories. Employing gravitational wave techniques such as the expected signal-to-noise ratio as well as considering effects from a variety of instrumental noise models, saddle trajectories and systematics...