The best way to do this is to hire a lawyer.  Just because you hire a lawyer doesn't mean you have to sue;  the lawyer can do the haggling with the insurance company for you.  You're much less likely to get "low balled" this way, because the insurance company knows the lawyer will spot that, even if you wouldn't;  also, the lawyer should know how to make sure that your claim is fully presented (in terms of proof of loss).  There's a very good chance that you will end up with more money, even after paying the lawyer, than if you do this on your own.