Not to supercede Aswartz on this - no doubt he could give a considerably more nuanced (and complete) opinion on the copyright thing, but I've a good bit of experience on the practical aspects of copyright as it applies to photography, as I've been doing it (photography) for about 30 years or so.
In general, and with the exceptions noted, if you take the photograph, you own the copyright by default. The exception is that if you enter into a legal agreement with the owner of the object (or person, as the case may be) to sign over the copyright for specific considerations, such as the limited right to use the owner's name in a description of the object in a publication. Another exception is the use of a photograph of a recognizable individual for commercial purposes - i.e., you can't take a close-up picture of Jeff Gordon at a NASCAR event and use it for financial gain without his permission.
However, that restriction does not apply to the owners of physical objects. For example, you can take an image of the exterior of an historic building from a public area (like the street) and publish with an identification in a magazine, regardless of the owner's feelings on the issue.
Obviously, however, the best route on something like this is the permission of the owner of the object in writing. My own personal experience on this with antique owners in the local area is that some are thrilled and proud that someone is interested in photographing and reproducing their heirloom, and some want nothing to do with it. I'd bet we'd find a similar situation with Museums - those that are famous may be a lot less interested (particularly if they're granting access to reproducers in exchange for a fee or licensing agreement), and some that are out-of-the-way may love the idea of getting some publicity for their organization.