Nanoperforated ZrO2 membranes, produced via organic/inorganic self-assembly using block copolymer micelles, serve as template for a Co/Pt multilayer stack with out-of-plane magnetic anisotropy. The deposition of the magnetic film results in an array of magnetic nanodots surrounded by a continuous magnetic film. These magnetic dots are found to be in a single-domain state and appear as magnetically exchange isolated from the surrounding film. The latter observation can be related to the specific morphology of the nanoperforations. In addition, strong domain-wall pinning of the continuous magnetic film at the locations of the nanoperforations was observed. Therefore, this approach is promising to create a percolated magnetic medium, which is considered as future recording media.