Read your renters or homeownwer's policy carefully - you might be covered already, especially if you don't gig the gear. Some policies will balk at covering gear as personal property if you gig it. They will say it is business equipment, and then they weasel out of paying a claim.
Better yet, talk to someone at the insurance company and have them show you where on the policy it says exactly what they will do in case of a loss. This is important whether you try to use an existing personal property policy or get a standalone instrument policy.
Also, policies vary regarding what they consider "antique" and they either won't cover it or they will dramatically reduce its replacement value. They often consider older gear like an old rocking chair, negating any vintage value.