AMEX cards ( issued by AMEX itself ) in general have the most consumer friendly claim process.
You can file a claim online with AMEX.
Also As AMEX themselves has access to your statements, they often already have all the info they need after you tell them when and where you purchase it from.
On the other hand, Visa / MC often require you to call-in to file a claim, and then mail-in / fax-in the original receipt, the statement, and other paperworks.