Originally Posted by Calum

This has sort of happened to me before, travelling on BA1. The system between the airlines and the CBP went down around an hour before the flight, everyone who didn't have a visa stamped in their passport/non US citizens were offloaded. We all watched our bags come out of the hold and at the same time, the boarding agents said if any of us were able to find their ESTA numbers/a copy of the esta, they can phone someone to confirm it and reload us.

Since then I have an album on my phone with a copy everything for quick reference.