CFD simulations of floating wave energy converters are computationally very heavy. This paper deals with a straightforward attempt to cut down on the computational effort by using adaptive mesh refinement (AMR). We investigate the use of AMR for simulations involving floating bodies inside the open-source finite volume framework OpenFOAM. A simple error indicator based on the pressure jump over cell faces is used to drive the AMR. First the use of the error indicator is illustrated for propagation of a very steep stream function wave. Then the AMR technique is applied to two cases of floating bodies: (i) a floating box and (ii) a bottom reacting point-absorber. As expected the AMR significantly reduce the number of cells in the computational meshes and subsequently lower the  computational effort.