How can I obtain and install duplicate license keys when copying to a new Mac? I have a desktop Mac and am getting a laptop, and I intend to use the migration assistant to copy software from the existing Mac to the new one.

I would like to obtain duplicate license keys for the software on it: Serene Screen 3, Microsoft Office, VMware Fusion, Windows XP (guest OS), Windows 7 (guest OS), and possibly others.

I don't know that the procedure for purchasing and installing duplicate license keys will be the same but how, for the software listed, can I purchase and install a duplicate key?
If you're using Migration Assistant, the software will stay licensed, and if you intend to wipe and repurpose the old computer it's likely you're in the clear as far as licensing goes. 

The Windows guest OSes won't notice any change: VMware's virtual hardware won't change, so they'll be totally oblivious to the migration.

I know from past experience that Microsoft Office works fine after Migration Assistant runs. I'm not sure about Serene Screen or VMware, but I've never had any trouble with any licensed software after Migration Assistant, including notoriously picky stuff like Photoshop or LabVIEW.

Now, on the other hand, if you simply want to clone the software and use it on both machines, you could probably get away with using the same keys, but you should check the license to see if that's allowed. If it's not, it should be as easy as buying a new license key and just replacing the old one on one machine.