I have a handful of pieces in my collection covered by my renter's insurance and it barely increased my monthly cost, you will however need a letter of appraisal for said pieces in order to get them covered which will be a flat fee depending on the appraiser. Ronnie, http://art.pirovinoprojex.com/, was great to work with and super helpful in getting me the correct documents. Definitely recommend reaching out to him!
Just a public service announcement: GET RENTER'S INSURANCE! In the wake of the fires here in CA the people who are going to have one of the hardest times are renters who are uninsured. By and large renter's insurance is so cheap that it will barely be a blip on your radar. My wife and I didn't get it until our rental in NY was flooded and we were S.O.L. Now that we're landlords we require our tenants to carry renter's insurance.
I looked into this a while back and I was told by my insurance company that I would have to have some kind of special policy because of the high dollar value of my collection and due to the fact that they were just regular belongings in the house. It may not be covered under your regular homeowner's/renter's policy so be sure to do your due diligence!
Considering everyone in this thread mentioned renter’s/homeowner’s insurance but mentioned nothing about possibly needing a special policy that covers collections, it may not be as obvious as you’d think.