Original Member and FlyerTalk Evangelist
Join Date: May 1998
Location: Kansas City, MO, USA
Programs: DL PM/MM, AA ExPlat, Hyatt Glob, HH Dia, National ECE, Hertz PC
Posts: 16,579
I don't know an automated way to find a high fare, but I know that one of the most expensive fares I have ever seen, even with advance purches is MSY-CHS. I just checked and the cheapest advance purchase fare on UA for that route is just under $830.
Finding one much higher than that may be a great challenge as MilageAddict said.