This paper examines lateral capillary interactions between millimeter- and sub-millimeter-sized objects floating at the interface between perfluorodecalin (PFD) and water. It describes methods-both experimental and computational-that allow the shape of the interface to be described for various geometries of the interacting objects. From these shapes, it derives the energy profiles characterizing the lateral capillary interactions. This work also demonstrates a new experimental method of imaging and studying menisci, and of studying capillary interactions between objects.