JMS, if you want an upgrade FIRST I would
request it when you make the reservation.
(Obviously the higher tier in an airline's
program, plus seat availability the better
the chances for upgrade.)

Then either the night before when you confirm
your flights or at the check-in counter I would say are there upgrades available.

As PremEx I have a very good upgrade rate.
But I still carry two coupon books of certificates and a few times this year the
gate agent asked for the certificates. (another CATMAN tip: always carry the upgrade
certificates with u, and have them within
easy reach.)

I assume it's teh same situation with AA
and COntinental. Good luck! CATMAN