The work presented in this thesis is centred around Symmetric Achromatic Variability, a rare phenomenon observed in the light curves of blazar sources. SAV is hypothesised to arise through gravitational milli-lensing when relativistically moving components traverse the lensing caustics created by some intervening massive object(s). It was first identified due to the presence of symmetric U-shaped features within 15GHz blazar light curves produced using the Owens Valley Radio Observatory 40m telescope. In this thesis I present a model to describe the light curve of a lensed blazar source. I then introduce a fitting procedure which uses nested sampling to fit this model to blazar light curves, with the goal of using this procedure to identify SAV within the the OVRO data set. I also demonstrate how this procedure can then be used to generate artificial blazar light curves based on real OVRO data. I then show the results of running the fitting procedure with both real and simulated blazar light curves. Additionally, I propose a framework for a transdimensional alternative to standard nested sampling algorithms, where the number of model parameters, N, is itself included as a free parameter. Such an approach could have wide-ranging applications, including for the problem of SAV identification. I describe the process by which we explore the parameter space, including the introduction of a novel concept - the 'flattened' particle space. Using both data and an analytical approach, I investigate the performance of this method. Finally, I detail an ongoing campaign to monitor the SAV candidate J1415+1320 using e-MERLIN at both L- and C-band, in order to gather evidence for or against the achromaticity of the SAV events. I then present and analyse light curves produced from the most recently available data.