Microlithography methods and apparatus are disclosed that allow reticle deformations to be measured and corrected quickly and accurately. Multiple alignment marks (comprising a “first set” and “second set” of reticle-position-measurement marks) are formed on the reticle. A first set of reticle-deformation data is obtained by detecting the positions of at least some of the first set of reticle-position-measurement marks using an inspection device that is separate from the microlithography apparatus with which the reticle will be used for making lithographic exposures. The first set of reticle-deformation data is stored in a first memory. The reticle then is mounted in the microlithography apparatus, in which a second set of reticle-deformation data is obtained by detecting the positions of at least some of the second set of reticle-position-measurement marks. The second set of reticle-deformation data is stored in a second memory. Lithographic exposures are performed, using the reticle so measured, while correcting the respective positions and/or deformations of the respective subfields on the fly, according to both sets of reticle-deformation data recalled from the respective memories.