First of all thank you to everyone for your responses. It's clear I need to provide some additional information.
The original ticket was purchased by me using an Amex card a couple of years ago. I bought a full fare ticket because I was concerned the dates might change. This turned out to be correct as the people I was going to meet kept pushing the dates back. Some of the changes didn't result in a higher price but some required an add collect. I used whatever Amex card happened to be in my wallet to pay the upcharge as they were modest, around $40-70 dollars. This went on for a substantial period of time. Eventually it became clear the trip wasn't going to happen. The ticket sat in my drawer until September when I got around to dealing with it.
When I received the confirmation for the refund from United it was split among three Amex cards, two for the add collects and a third for the bulk of the fare. When the refund for the bulk of the fare didn't appear on any of my current cards I called Amex. They attempted to track down the card from the last four digits of the number that United had provided but couldn't find the card. They said this is not unusual as accounts which have been closed fall off the system and they asked me to request the entire card number from United, which I did.
I have the ticket number for the ticket I refunded. I don't have a record of the original ticket since it never occurred to me I'd need it (lesson learned).
United knows the account they credited the refund to. They also know the reference number of the transaction. Unfortunately I am unable to get United to provide that information to either myself or to American Express. While in hindsight I can see why United might not want to provide me with the full credit number to which they credited the bulk of the refund that's what American Express asked me to request them to do. United could have responded that's they'd be happy to work with Amex to track down my refund but they didn't. Instead they told me to call Amex again knowing that Amex needed additional information from United to proceed. Not particularly helpful.
I've since asked United to provide the Reference number. So far they've failed to respond. Once again, not particularly helpful.
I'm not asking United to do anything more than provide the information they have which is needed to track down a refund that hasn't gotten to where it was supposed to. Supplying the reference number or contacting Amex and providing them with that and/or the credit card number would quickly resolve the situation.
I've opened a dispute with Amex but United has taken something that is would have been simple and making it extremely difficult simply just because they can't be bothered providing the reference number.
As I said any suggestions would be welcome.