I recently added a second email domain to our exchange 2010 server and set myself up an email address for the new domain.
Receiving emails works very well.
I used this guide to setup send-as on the Outlook client link
However I get the the following error when sending from the new email address
You can't send a message on behalf of this user unless you have permission to do so. Please make sure you're sending on behalf of the correct sender, or request the necessary permission. If the problem continues, please contact your helpdesk.