[Richard Flynn]

Yes, this is what a ‘Personal’ licence does—buy an OmniGraffle licence, and put the number in to your installation of OG on both your home desktop and your laptop, being sure to choose the ‘Personal’ option. That way you can use the application on both machines pretty seamlessly, as long as you don’t try to run them at the same time (so quit OG on one machine before opening it on the other).

Because you are using a ‘Personal’ licence, the licence will only apply within the one user-account that you install it in on either machine. So, if you have other user-accounts on either of your computers (perhaps used by other members of your family), those users won’t be able to use OmniGraffle without them buying a licence for themselves (which they would then be sensible to install as a ‘Personal’ licence).