As far as I know, there are no successes. Most attempts couldn't have open borders, because everyone would leave.
(And yes, there are lots of other factors, like corruption and the natural resource curse.)
Essentially, claiming that your economic theory will only work once a dramatic, complete, state-wide change as occured is a non-starter. Nations advance by degrees, and if there aren't small moves that can be made towards the goal that provide evidence that the theory is sound, it would be foolish to believe that big moves will fair any better.
I would genuinely like to see examples of where libertarianism ideals have been tried on a small to medium scale and been successful. And if there aren't any, same question as to jasonisalive: why is there such confidence among libertarians that it works in the real world?
To me it seems that only you talk about libertarians, while jasonisalive talked about generic economic research.
(Wikipedia confirms my belief that libertarians are quite heterogeneous and it is more of a political philosophy/ideology than about economy anyway.)