This work presents a study of two Herbig Ae transitional discs, Oph IRS 48 and HD 169142; which both have reported rings in their dust density distributions. We use Keck-II/NIRC2 adaptive optics imaging observations in the L' filter (3.8 µm) to probe the regions of these discs inwards of ∼ 20 AU from the star. We introduce our method for investigating these transitional discs, which takes a forward modelling approach: making a model of the disc (using the Monte Carlo radiative transfer code RADMC3D), convolving it with point-spread functions of calibrator stars, and comparing the convolved models with the observational data. The disc surface density parameters are explored with a Monte Carlo Markov Chain technique. Our analysis recovers emission from both of the discs interior to the well known optically thick walls, modelled as a ring of emission at ∼ 15 AU in Oph IRS 48, and ∼ 7 AU for HD 169142, and identifies asymmetries in both discs. Given the brightness of the near-symmetric rings compared to the reported companion candidates, we suggest that the reported companion candidates can be interpreted as slightly asymmetric disc emission or illumination.