This one has been sitting in my drafts folder for a while but last year I was experimenting with our SharePoint environment and thought it would be a cool idea to have a view of our web mail and calendar come up into our SharePoint homepage as web parts. Now if you are running SharePoint 2010/2013 you can simply use the Outlook OWA web parts to display what you want to a degree but by using a web page viewer web part and specifying the URL we can have a better degree of control on the output of the page.
So start by adding a web page viewer web part to your page and point the web part to your exchange server hosting Outlook Web Access. The following is an example of a URL that you can use:
Exchange 2010
https://owaurl/owa/?cmd=contents&module=Publicfolders&fpath=School%20Calendar&view=weekly
Exchange 2013
https://owaurl/owa/#path=/calendar
For more information on how to format the links and available flags please follow this link http://technet.microsoft.com/en-us/library/bb232199.aspx. I hope that has helped some people in bringing better looking mail access to their share point environments.