I would propose a free-trade agreement with the UK. No loss of sovereignty, no stupid EU regulations and bureaucrats, no restrictions on what can be called "sausage" -- just trade. I would offer a similar deal to anyone else who wanted to leave.
Actually, when Obama visited, I would have been tempted to offer it to Britain at that time. Why was the US President so hell-bent on encouraging closer ties between Britain and Germany when he should have been working to improve the relationship between the UK and the US.
I will admit that I am not thrilled with the anti-immigration tone of the Brexit vote, but the EU is a package deal, and there is a lot of bad with the good in the package. Here is a good list of reasons to vote for Brexit (hat tip maggies farm)