Hello there,
 
I was wondering if there was a way to get a notice message when your mailbox is almost full so it doesn't run full without anyone noticing.

I Didn't find anything like that but maybe you can help me out.
 
Looking forward.

This is built-in feature of Exchange Server itself where it sends automatic warning email to the mailbox which is about to consume the mailbox space allocated to it. So, you do not have to worry as all your clients will receive warning email prior to reaching their storage limits :)