If you will be checking in yourself later that day a call to the hotel front desk has worked for me before (Marriott), since they already had my CC on file for the reservation. When I arrived a few hours later I dropped by the front desk and showed them the physical credit card and my ID.
If you won't be checking in yourself, with Marriott you used to be able to call the local hotel to arrange billing ahead of time. My office used to do this for employees who were traveling without a Corporate Amex. If I recall correctly, my clerk had to fax over a photo copy of my Amex, but it might vary depending on the property.
My experiences were a few years ago, though, and were only with Marriott. I'm surprised/disappointed that there's not a better solution these days. 
