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How do you go about a suspicious Amex charge that has been posted? When it was still pending, I asked customer service to monitor the charge.
For almost all credit cards, you would not be responsible for unauthorized charges. So once the charge has been posted, verify if you recognize the transaction - if not, call the customer care and they most likely will transfer you to fraud department and they will investigate the charge on your behalf.
Talk to the fraud department. They helped me when I had a suspicious charge.
Historically, I have reported cards stolen, even before the charge posts, if I know for certain it isn't anything I initiated. I just had two charges made yesterday for online orders from beauty companies on my Citibank card. They are still pending but I reported the card stolen this morning to cut off any more charges (and to hopefully get the merchants to stop shipment).