A variety of methods are developed for characterising the free energy landscapes of continuum, Landau-type free energy models. Using morphologies of lipid vesicles and a multistable liquid crystal device as examples, I show that the methods allow systematic study of not only the most relevant minimum energy configurations, but also the transition pathways between any two minima, as well as their corresponding energy barriers and transition state configurations. A global view of the free energy landscapes can then be visualized using either a disconnectivity graph or a network representation. Different forms of free energy functionals and boundary conditions can be readily implemented, thus allowing these tools to be utilised for a broad range of problems.