Sr2CuWO6 is a double perovskite proposed to be at the border between two- and three-dimensional magnetism, with a square lattice of S = 1/2 Cu2+ ions. We have used inelastic neutron scattering to investigate the spin wave excitations of the system, to find out how they evolve as a function of temperature, as well as to obtain information about the magnetic exchange interactions. We observed well defined dispersive spin wave modes at 6 K, which partially survive above the magnetic ordering temperature T-N = 24 K. Linear spin wave theory is used to determine the exchange interactions revealing them to be highly two dimensional in nature. Density functional theory calculations are presented supporting this experimental finding, which is in contrast to a previous ab initio study of the magnetic interactions. Our analysis confirms that not the nearest neighbor, but the next nearest neighbor interactions in the tetragonal ab plane are the strongest. Low incident energy measurements reveal the opening of a 0.6(1) meV gap below T-N, which suggests the presence of a very weak single ion anisotropy term in the form of an easy axis along (a) over cap.