Linked data (LD) have the capability to open up and share materials, held in libraries, archives and museums (LAMs), in ways that are restricted by many existing metadata standards. Specifically, LD interlinking can be used to enrich data and to improve data discoverability on the Web through interlinking related resources across datasets and institutions. However, there is currently a notable lack of interlinking across leading LD projects in LAMs, impacting upon the discoverability of their materials. This research describes the Novel Authoritative Interlinking for Semantic Web Cataloguing in Libraries (NAISC-L) interlinking framework. Unlike existing interlinking frameworks, NAISC-L was designed specifically with the requirements of the LAM domain in mind. The framework was evaluated by Information Professionals (IPs), including librarians, archivists and metadata cataloguers, via three user-experiments including a think-aloud test, an online interlink creation test and a field test in a music archive. Across all experiments, participants achieved a high level of interlink accuracy, and usability measures indicated that IPs found NAISC-L to be useful and user-friendly. Overall, NAISC-L was shown to be an effective framework for engaging IPs in the process of LD interlinking, and for facilitating the creation of richer and more authoritative interlinks between LAM resources. NAISC-L supports the linking of related resource across datasets and institutions, thereby enabling richer and more varied search queries, and can thus be used to improve the discoverability of materials held in LAMs.