So we all enjoyed the Obama speech ... now time for work again ...  

I was trying to do a restore of site collection with a different name on our test server and found out a nice error message which is:

This error :

No content databases are available for this operation. Create a content database
, and then try the operation again. To create a content database, click "Content
 databases" on the Application Management page, select the Web application to us
e, and then click "Add a content database".

The error in no way shows what has happened. I went through quite a pain to find out. What i found out is sharepoint stores each list and library with a specific guid.
If we try to restore the site collection with different name, the lists inside gets replicated inside the database which the sharepoint will never allow.

Resolution:

The best way to solve is to use a new content database for the copied site collection. Which means to use a different web application. Else you need to use either -overwrite method or just delete the existing site collection :-).