These are for JMP17 (should also work for older JMP versions but not for JMP18 (it has a bit different paths)) on Windows. Before doing any of these steps, take backups of the current files.
Run JMP once on the new laptop and make small change to preferences.
If the username will be the same, you should get quite far if you just copy JMP folder from %appdata%/SAS (C:\Users\<username>\AppData\Roaming\SAS). Some of these files could potentially break something, so you might just want to copy over files one by one (haven't yet happened to me).
If you have JMP Pro you will most likely want to copy also that (if you have JMPPro you want to copy "non-pro" folder as it contains a lot of needed files)
If the username changes (or paths in other way) you will have to fix addinRegistry.xml file manually (or reinstall addins). You can take a peek into different files if you wish to see what they store. Below are few files which I think contain information you want to move over
In addition to that if you might have some files saved to your JMP installation folder (Maps come to my mind) which you might want to check. There could also be some files "hidden" in program data (%programdata%/SAS).
Recent files won't be moved over as those are stored to registry (you can get them from there if you really want to).
-Jarmo