Thanks Judy,

That doesn't work.   I have that setting turned off so that invites don't get
deleted when I respond to them.   But even with that setting off, meetings
you decline stay in your calendar.   The only workaround I've found is to do
the following:
1. Decline a meeting that I can't attend because of a conflict and send my
response so the meeting organizer knows I won't attend
2. Go back to my inbox, open the invite again, change the "show as" time to
"free",  and accept the same meeting (but don't send a response to the
organizer).   That puts the meeting back in my calendar.
3. If my conflicting meeting gets cancelled, I then can open the meeting I
declined and accept it again, this time sending a response to the meeting
organizer.

What would be far more helpful is for Outlook to decline a meeting like you
currently can (for meetings you don't want to go to regardless of whether
you're free or not) or decline a meeting but keep it in your calendar and
showing as "free" time (for meetings you'd like to attend if your schedule
frees up.  

Then, if the conflicting meeting was cancelled, Outlook could alert the user
that there's another meeting at that time and allow them to accept or decline
it.

This is a major issue for me since I'm often overbooked at any given time
and meeting schedules tend to change frequently.