Note NOV2020: If you just copy/paste the last file "/Library/Preferences/com.microsoft.office.licensing.plist" as instructed above, it should work as well. For transparency, this was tested on an old mbp with El Capitan and incoming connections blocked with Firewall (unsure if Firewall would affect outcome).
If this doesn't work for you (ie. you probably don't own a legitimate copy of the program) I'm afraid you're out of luck, I believe the licensing information may be stored in the com.microsoft.office.licensing.plist file which is located in /library/preferences but it's encrypted so... good luck with that.
When you run Word, Excel, PowerPoint or Outlook 2011, it checks /Library/Preferences/com.microsoft.office.licensing.plist . If that file is not valid (such as after doing a fresh install of Microsoft Office 2011), it launches /Applications/Microsoft Office 2011/Office/Microsoft Office Setup Assistant.app. Microsoft Office Setup Assistant checks whether the DVD from which you installed is a volume licensed copy; if it is, it silently populates that plist and quits (allowing the app you initially started to start up); if it is not, it prompts you for a product key and activation.
1. Copying /Library/Preferences/com.microsoft.office.licensing.plist from a working install. You can do this using your favorite software depolyment tool, such as Munki. Please note that importing it as a Managed Preference (MCX) into Workgroup Manager (and probably Profile Manager) does not help. The file needs to be physically present on the client machine.