It is now possible to search through your completed trades by username in your trading center, which will be useful to those of you who have like a million pages of trades . Thanks to DisabledLlama for the suggestion.
While I was there I improved it so that it shows a little summary under each trade of how many pets and items are involved on each side, which should help you find the trade that you're looking for. Or maybe show you which trades you don't even need to bother looking at right now.