Mesh adaptation methods can improve the efficiency and accuracy of solutions to computational modeling problems. In many applications involving quadrilateral and hexahedral meshes, local modifications which maintain the original element type are desired. For triangle and tetrahedral meshes, effective refinement and coarsening methods that satisfy these criteria are available. Refinement methods for quadrilateral and hexahedral meshes are also available. However, due to the added complexity of maintaining and satisfying constraints in quadrilateral and hexahedral mesh topology, little research has occurred in the area of coarsening or simplification. This paper presents methods to locally coarsen conforming all-quadrilateral and all-hexahedral meshes. The methods presented provide coarsening while maintaining conforming all-quadrilateral and all-hexahedral meshes. Additionally, the coarsening is not dependent on reversing a previous refinement. Several examples showing localized coarsening are provided.