I know that you are not supposed to put valuables into checked baggage, but in some cases it is necessary. For example if you have large valuable items that do not fit in carry-on or if you have enough valuable items that you can not fit them all in carry-on.
My understanding is that while airlines do accept liability for baggage, they typically exclude valuable items such as electronics, jewelry etc. and the liability dollar limit is quite low. I've also heard they will won't accept liability for loss, damage or delay caused by "security searches." Here for example is American Airlines Baggage Liability Limitations.
Given that it seems that airlines have limited their liability to the extent that they probably won't pay for anything valuable -- or perhaps anything at all if they can blame the "security procedures" -- what is the best insurance to protect yourself? I'm from the USA and interested about insurance for international travel.