We deal with solid parallel-plate UV-based nanoimprint lithography (UV-NIL) using rigid quartz stamps and spin coated substrates. Achieving homogeneous imprints with a thin residual layer are important for a succeeding reactive ion etching (RIE) step. Since the solid stamp and the substrate are not perfectly flat and mounted on solid parallel plates giving them little chance to adapt and compensate for the unevenness and causing additional distortions, this is difficult to achieve. We investigated the bending of a rigid quartz stamp during imprinting and the effect of a thin compliant layer located below the substrate with finite element simulations and compared them with experimental results. We show that a close contact of stamp and substrate can be achieved with a correctly designed compliant layer and using a commercially available EVG®620 mask aligner.