Libraries and archives across the globe have adopted the International Image Interoperability Framework (IIIF) to make high-resolution images of their digitized map collections available to the public. These images are often not (yet) georeferenced, which limits their findability, usability for spatial analysis and integration with other geographic data. IIIF maps can be manually georeferenced in Allmaps Editor by masking images and indicating Ground Control Points (GCPs). While effective, this process is also time-consuming and repetitive, especially when dealing with large map series, consisting of many sheets following a uniform layout. We therefore propose a novel and semi-automated method for georeferencing map sheets of such map series. The proposed approach employs computer vision techniques to detect the neat lines of map sheets. The crossing of these neat lines often corresponds to well-defined geographic coordinates in a sheet index, making them ideal candidates for georeferencing. By harnessing the inherent structure of map series, our approach reduces the manual labour involved in the georeferencing process. The method is adaptable and capable of handling slight variations in the layout of sheets. We demonstrate the effectiveness of our approach through a series of case studies involving different map series from various institutions worldwide. These results highlight the potential of our method to enhance the digital accessibility and re-usability of historical map collections.