Angle-dispersive x-ray-diffraction and x-ray-absorption near-edge structure measurements have been performed on CaWO4 and SrWO4 up to pressures of approximately 20 GPa. Both materials display similar behavior in the range of pressures investigated in our experiments. As in the previously reported case of CaWO4, under hydrostatic conditions SrWO4 undergoes a pressure-induced scheelite-to-fergusonite transition around 10 GPa. Our experimental results are compared to those found in the literature and are further supported by ab initio total-energy calculations, from which we also predict the instability at larger pressures of the fergusonite phases against an orthorhombic structure with space group Cmca. Finally, a linear relationship between the charge density in the AO8 polyhedra of ABO4 scheelite-related structures and their bulk modulus is discussed and used to predict the bulk modulus of other materials, like hafnon.