I've seen the situation where a unit has used all its movement points to get to the city with the Barracks, and then another unit of that same type does Shift-U, upgrading both (or all).
Another trick: when you get the Science Advisor telling you that another Tech has been learned, select 'Show me the Big Picture' which takes you to the F6 screen, then go to F1, select cities with units that can now be upgraded, right-click on those units from the city-display screen and upgrade them. You can't do Shift-U this way, but the units are upgraded and can be moved and used in attacks on the same turn that the Technology allowing the upgrade has been researched. This worked in CivIII (haven't tried it in PTM), and is really useful when Chivalry or Military Tradition are researched.