Outlook Calendar used to work correctly offline. I could create new appointments while offline, and they'd sync when I went back online. Then one day I started receiving this error message:

Microsoft Office Outlook
Could not save item.  The connection to Microsoft Exchange is unavailable.  Outlook must be online or connected to complete this action.

I don't know why, or how to really fix it, but here's a work-around.

In the lower-right corner of the Outlook window, where it says "Disconnected" -- change that drop-down to say "Work Offline".