Activating Trados Studio 2015 on a second Mac

I am running Trados Studio 2015 on an Apple iMac using VMWare Fusion to run Windows 7 as a virtual system from an external SSD. So far, so good, for several years now. Now I'm going overseas for several months and want to transfer Trados to my new MacBook Pro, using the same external SSD to run the same copy of Windows 7. When I connect the SSD to my MacBook and start up Windows, it's all fine, but Trados will not start up and requires an activation code. I have tried deactivating Trados on my original iMac, but when I then try to activate it on my MacBook, activation fails because the number of remaining activations is 0 (it says).

Just now, I tried again, failed again, and then found that I couldn't start up Trados on my original machine either -- same message. So I have gone through the Return License steps and am now waiting to see whether that will allow me to start up Trados on my iMac. (I really hope so as I'm in the middle of an urgent job!) But is there a way for me to safely try again to activate Trados on my MacBook?