If your gun is stolen immediately tell local coppers. You’d want to do the same if your car was stolen — and then used in a drive-by shooting.
Don’t bother insurance unless it is covered by your policy.
Mind, if gun is stolen you need to be able show that it was not your fault. E.g., in CaCaLand all guns must be locked up when in a car, and in the house if kiddies can get into the house. If this crappola does not apply to you (e.g., car was broken into and gun taken) make sure you tell coppers and provide them with the serial number.
Unless you have a sizable collection stolen it is probably not going to meet your deductible.
If you have such a collection you would have to declare it on your policy for it to be covered. This means each firearm described and serial numbers documented.
At least on my policy.