I recently purchased a separate insurance policy to cover my collectibles (sports memorabilia, comics and Star Wars toys). Chances are, your homeowners/renters insurance doesn't cover them, beyond the amount covering personal belongings which you'll also need to cover the replacement of clothes, furniture, etc. I checked with the insurance company that I purchase homeowner's insurance from, and it was quite expensive to cover the additional items in my collection.
I read several recommendations on different web sites and publications for Collectibles Insurance Services (http://www.collectinsure.com/). The web site will give you a quote for insurance covering the value of your collection. They don't require an appraisal, or even an itemized list. Just a dollar amount to be covered, as well as a general description of the collection (stamps, firearms, baseball cards, etc). You will need an itemized list to make a claim though.
Last week I filled out the application available online, and emailed it in. I then called to give them my credit card number. I have not yet received the policy, but my card has been charged, so I'm assuming I'm covered!
I guess I can't offer a full recommendation until I try to make a claim, which hopefully I never need to do. But, I feel better knowing that my Iron Man #1, carded Power of the Force Jawa and 1956 Hank Aaron card are covered should anything go wrong.