First off, sorry for your loss OP.
With the growing concern of theft at major events and a couple close calls with my cards, I specifically asked my renter's insurance provider if my collection was covered completely under my policy. Even though my other possessions are covered completely, there were loss limits on certain categories of items. I was told my cards would be considered under philatelic items (i.e. stamp collections) and that the loss limit was $1,000. They did offer additional coverage, but trading cards weren't considered a coverable category (although stamp collections were, for some reason).
Not liking the answers I was hearing, I went with a company that specializes in collectibles. I found at least two of them that specifically covered trading cards: American Collectors Insurance and Collectibles Insurance Services. The premium from either for $20k of coverage was ~$120 a year and well worth the additional peace of mind. No appraisal required, but they did require photo proof of any single item over a certain limit. American Collectors also has an online interface that lets me upload inventories and photos for collection tracking which I found to be useful.
Hope everything works out for you in the end. For everyone else, I recommend you specifically ask your insurance company if your cards are covered and for how much.
Best advice.
Also, some insurances have appraisers that will come and look at your collection and appraise it for insurance purposes.
I've had my collection appraised and covered by a separate insurance for theft and fire + water damage, because it isn't covered by my house owners insurance.