Germanium membranes and microstructures of 50-1000 nm thickness have been fabricated by a combination of epitaxial growth on a Si substrate and simple etching processes. The strain in these structures has been measured by high-resolution micro-X-ray diffraction and micro-Raman spectroscopy. The strain in these membranes is extremely isotropic and the surface is observed to be very smooth, with an RMS roughness below 2 nm. The process of membrane fabrication also serves to remove the misfit dislocation network that originally forms at the Si/Ge interface, with benefits for the mechanical, optical and electrical properties of the crystalline membranes. ; This work was supported by the EPSRC, Projects. EP/F040784/1, and EP/J001074/1; ERC grant #202735, “NonContactUltrasonic”; NANOFUNCTION Network of Excellence, funded by the European Commission 7th Framework Programme (ICT-FP7, #228464). ; Peer Reviewed