Macbook pro 15 inch mid 2012 outlook 2011
You can archive your Outlook:Mac 2011 emails, although it's a bit fiddly to do.


In the Finder, create a new folder where your Outlook archive will live.  I've always called mine "Outlook backup [date]" (ex: "Outlook backup 2016-04-18").
Inside this folder, create a folder structure that's the same as what you want to backup from Outlook.  For example, if you have a folder named "2015 emails" and you want to back it up, create the new folder "2015 emails" inside the "Outlook backup 2016-04-18" folder.  You can then create "January", "February", etc folders inside the "2015 emails" folder.  
Arrange your desktop: have an Outlook window open and a Finder window open such that you can view both of them.
In Outlook, select one of the folders that you want to archive.  Drag that folder to the corresponding folder in the Finder.  In your Finder window, you'll see files named "Folder name.mbox" get created.  If you've got a lot of email in your folder, it'll take awhile for this to do, and there's no progress bar to tell you when it's done.  
Repeat step 4 until you have backed up all of your folders.  Delete the folders that you no longer need.


The contents of "Folder name.mbox" are all of the emails that are in that folder.  The contents of "Folder name.mbox" does NOT include subfolders, so you will need to repeat these steps for the subfolders.  

Alternately, if you don't want to create a big folder structure, you could do this slightly differently.  Create the "Outlook backup 2016-04-18" folder.  When you drag the folder to the Finder and it creates the "January.mbox" file, you could rename that file to "2015 emails - January.mbox" (or something else to indicate that it's a subfolder of the "2015 emails" folder).  

Now what do you do with all of these .mbox files?  The good part about .mbox is that it's a standard file format for storing emails, and pretty much any email client can import them.  If you need to view the contents of your .mbox files again, you can simply drag them back into Outlook, and your folder will be there with all of its email (except for the subfolders, which you'll need to drag into Outlook separately).  When I need to bring back all of the email in subfolders, I find it easiest to add the top-level folder first, and then add the subfolders.

If this sounds like a lot, there is an application called Mail Archiver X for which I've received many recommendations.  I haven't tried it myself; the $40 price tag is enough for me to drag my Outlook folders to the Finder manually.