I share a Calendar with a co-worker.  I want the reminders to pop up on both of our computers, but they're only showing up on mine.  How do I fix this?

Don't do it that way.  Ensure that you're both invited to all meetings.

Hi,

It is by design. Outlook only supports firing reminders in your own mailbox or default PST file. The reminder doesnt work for shared calendar though the user has Owner permission of this calendar folder. Reminders are available only for items stored in the main calendar.

Please consider Ed's suggestion to also add another user as an attendee for this meeting. Then the reminder would pop up for this meeting attendee.

Regards,