Due to advances in digitization technology, documentation efforts and digital library systems, increasingly large collections of visual Cultural Heritage (CH) object data becomes available, offering rich opportunities for domain analysis, e.g., for comparing, tracing and studying objects created over time. In principle, existing shape- and image-based similarity search methods can aid such domain analysis tasks. However, in practice, visual object data are given in different modalities, including 2D, 3D, sketches or conventional drawings like profile sections or unwrappings. In addition, collections may be distributed across different publications and repositories, posing a challenge for implementing encompassing search and analysis systems. We introduce a methodology and system for cross-modal visual search in CH object data. Specifically, we propose a new query modality based on 3D views enhanced by user sketches (3D+sketch). This allows for adding new context to the search, which is useful e.g., for searching based on incomplete query objects, or for testing hypotheses on existence of certain shapes in a collection. We present an appropriately designed workflow for constructing query views from incomplete 3D objects enhanced by a user sketch based on shape completion and texture inpainting. Visual cues additionally help users compare retrieved objects with the query. We apply our method on a set of relevant 3D and view-based CH object data, demonstrating the feasibility of our approach and its potential to support analysis of domain experts in Archaeology and the field of CH in general.