I flew LHR-SFO on 28th August. My ESTA was automatically cancelled 5 hours before departure time. I was a little worried about entering the USA as I'm a UK citizen in a same-sex marriage with a US citizen. Thankfully, the process of getting my ESTA reinstatement was very smooth. I just needed to have my married certificate verified at the BA check-in desk. This took around 15 minutes and involved the BA calling the US Homeland security representative for the verification. The check-in staff then updated my details, and my boarding pass was printed with 'Homeland Approved ESTA' on the pass.
On arrival in SFO went through the normal passport check process at the booth. Was then politely escorted to a secondary area where my wedding certificate was checked and approved by another custom and border protection officer - all done in under 10 minutes.