Packages for semiconductor devices, packaged semiconductor devices, and methods of cooling packaged semiconductor devices are disclosed. In some embodiments, a package for a semiconductor device includes a substrate including a semiconductor device mounting region, a cover coupled to a perimeter of the substrate, and members disposed between the substrate and the cover. The package includes partitions, with each partition being disposed between two adjacent members. The package includes a fluid inlet port coupled to the cover, and a fluid outlet port coupled to one of the partitions.