Just as with other forms of property, museum property can be insured. Buildings, computers, and collection objects are all within the realm of museum insurance.
This document offers a clear explanation of insurance principles, procedures, and vocabularies. It was prepared for a talk at the 2009 annual meeting of the New England Museums Association (NEMA), which has many small museums as members. While it focuses on fine art in its discussion of collections, the principles are the same no matter what composes the collections.
Huntington T. Block created an insurance checklist for museums.
This insurance handbook, by DeWitt Stern, is a generic model for the kind of information you might expect to receive from your insurance company.
The Smithsonian Museum Conservation Institute offers this page of advice on getting estimates for conservation, repair, insurance, and appraisal.
The National Trust for Historical Preservation’s Preservation Leadership Forum offers this guidance on getting the right insurance for your historic building.