That's why I love my Amex. Their system seems to be intelligent with regard to this. When I charge a flight and/or hotel, my statement shows the passenger (me) the dates and the destination along with the airline/hotel. I also get an email a few days later asking if I want to purchase any additional travel insurances.
No need for me to call, the details of my travels are already in their system and I've never had my card questioned or refused.
If you're travelling on points and haven't charged a flight or hotel through your card, it certainly can't hurt to give a quick call.