Identifying closely related languages at sentence level is difficult, in particular because it is often impossible to assign a sentence to a single language. In this paper, we focus on multi-label sentence-level Scandinavian language identification (LID) for Danish, Norwegian Bokmål, Norwegian Nynorsk, and Swedish. We present the Scandinavian Language Identification and Evaluation, SLIDE, a manually curated multi-label evaluation dataset and a suite of LID models with varying speed-accuracy tradeoffs. We demonstrate that the ability to identify multiple languages simultaneously is necessary for any accurate LID method, and present a novel approach to training such multi-label LID models.