Outlook.com has an option of recovering deleted messages. Although this feature will try to recover as many emails as it can, it  doesn’t guarantee that everything deleted will be recovered. However it is still worth giving a try.
Here is how  :
Login to Outlook.com, from the left pane, in the Inbox section, click on “Deleted” folder.
Here, scroll down and click on “recover deleted messages”.
After a while, the deleted messages will show up in the “Deleted” folder. Move those that are important to Inbox since this folder is automatically emptied periodically.
Cheers.
[…] [For recovering deleted emails in Outlook.com, refer to this earlier article ]. […]