We have deposited epitaxial SrRuO3 (SRO) thin films on SiO2/Si substrates using biaxially oriented MgO templates produced by ion-beam-assisted deposition. The strain states of the SRO films are strongly affected by the crystallinity of the templates: the better the in-plane texture of the template is, the more in-plane tensile stress the films are subjected to. On the other hand, SRO films are relatively loosely strained with lattice parameters closer to bulk property if the templates have a broad in-plane alignment. The magnetization of the SRO films is well described by Bloch’s T3/2 law at low temperatures, which is well known as the result of spin wave excitation: M(T)/M(0)=1-AT3/2. The strained films show larger spin wave parameter A values, reflecting larger magnetization suppression. The suppression of magnetization in the strained films is attributed to the change in the magnetic coupling since this coupling is very sensitive to the interatomic distance.