We have investigated magnetoelastic coupling in Sr 2 (Fe 1−x Cr x )ReO 6 polycrystalline double perovskites. The end compound, Sr 2 CrReO 6 , shows a high ferromagnetic transition temperature of 635 K and is thought to exhibit a nearly half-metallic conduction band. We probed the unexpected high orbital moment borne by the Re atom by means of volume and anisotropic magnetostriction measurements in magnetic fields up to 12 T. Our magnetostriction results can be explained by the existence of a large spin-orbit coupling which, in combination with crystal-field effects, produces a singleion type magnetostrictive response. The Re orbital moment triggers a greatly enhanced magnetocrystalline anisotropy compared to other ferromagnetic double perovskites.From our magnetostriction data, the temperature dependence of the coercive field as a function of Cr-doping is obtained. We discovered that the coercive field increases as Fe is replaced with Cr, which is linked to a strong enhancement of the magnetic anisotropy. This suggests a close relationship between the Fe[Cr]-O-Re coupling and the magnetic anisotropy. We also analysed the impact of the Re orbital moment on the spin-dependent transport across Sr 2 CrReO 6 grain boundaries. The present work opens up the possible use of these compounds for magnetostrictive applications in a wide temperature and magnetic field range.