Abstract: High-quality membranes of complex oxide and complex nitrides are provided. Also provided are method of making the membranes by releasing films of the complex oxides and nitrides from an epitaxial heterostructure using metal islands on the surface of the films as strain-absorbing supports. The methods facilitate the release of flat, large-area membranes characterized by the absence of, or a very low density of, cracks and/or wrinkles. The released membranes are free of the surface organic residues that are present on membranes released with the aid of a polymer support.