Methods of making hardmask assemblies or other layered structures, and other masks, include providing an annular seal member between a first surface of layered structure, preferably a hardmask assembly, and a first clamp element, the hardmask assembly comprising at least a hardmask layer; and applying a force between the first clamp element and a second clamp element to hold the hardmask assembly between the annular seal member and the second clamp element. In addition, there are provided methods further comprising etching the first surface of the hardmask assembly within the bounds of an interior space defined by the annular seal member. Methods further comprise etching the substrate layer through the hardmask layer and/or removing the hardmask layer after etching the substrate layer.