The deployment of virtual expositions of accurately rendered, high quality 3D models over the Web is a common practice today in many cases of cultural heritage and arts initiatives. In the specific case of virtual museums, where the nature of the content opens possibilities that go beyond those of a single, localised physical exhibition, the availability of Web-ready content related to the project's collection of digital models becomes almost mandatory. Although desirable, presenting interactive content over the Web is not a simple task, and a large part of the current generation of 3D-Web technology, being tailor-made mainly for graphics-only applications, often imposes severe limitations on the possibilities for user interaction.As a result of these technological limitations, the user expects of the virtual exhibition, and very little has been explored so far about the potential benefits that the sense of touch could introduce in the interaction paradigm. We report here the results obtained from mixing high performance 3D graphics with haptic interaction in the context of several museum installations, as well as presenting a new generation of Web technology that makes it possible to deploy this type of content on the Web.