More and more cultural heritage institutions publish their collections, vocabularies and metadata on the Web. The resulting Web of linked cultural data opens up exciting new possibilities for exploring these cultural heritage collections. We report on ongoing work in which we investigate the estimation of relevance in this Web of Culture. We study existing measures of semantic distance and how they apply to two use cases. The use cases relate to the structured, multilingual and multimodal nature of the Culture Web. We distinguish between measures using the Web, such as Google distance and PMI, and measures using the Linked Data Web, i.e. the semantic structure of and semantic links between vocabularies. We perform a small study in which we compare these semantic distance measures to human judgements of relevance. Although it is too early to draw any definitive conclusions, the study provides new insights into the applicability of semantic distance measures to the Web of Culture, and clear starting points for further research.