What is the best way to move Microsoft Office 2011 to a new Mac?

There are no special steps. Install it using the installer just like you did on your old Mac. When prompted for the activation key, select "activate by phone" and input nothing, keep trying and it should provide a number to call.

Microsoft (unlike Adobe) does not have an automated system for licence deactivation. This has been a point of great angst among Mac users as it requires them to call Microsoft each and every time they move the Office application from one machine to another.

I believe the number in the US is: +1 (800) 936-5700. Your product support number may vary.

Here is a rundown on activation and product key information.

This worked for me: After an incomplete timemachine backup (I excluded the folder /System/Library) I had to do the following to get it working again on the same machine (I guess it should also work on your second Mac).

Beside the App that was installed to /Applications/Microsoft\ Office\ 2011 Restore these files from your previous installation:

/Library/LaunchDaemons/com.microsoft.office.licensing.helper.plist
/Library/PrivilegedHelperTools/com.microsoft.office.licensing.helper
/Library/Preferences/com.microsoft.office.licensing.plist

Source: this guide