Moving Coldfusion to new server

We are moving our websites from one server to a new one.  We have installed Coldfusion Enterprise 8 on the new computer with the same license number.  The 2 servers are supposed to be moved on Friday, June 28th.  They will obviously both be turned off for the move and restarted once they are moved.  We are continuing to test the new server before we switch the live site from the old server to the new.  I am afraid that when it is restarted, I may have an error pop up due to the fact that they both have the same license number on it.  Can you tell me what will happen and how to avoid any problems?