One of Edgar Rice Burroughs' least known works was a story "Beyond Thirty" (published in book form as "The Lost Continent"). Written in the middle of WW1, ERB supposes a world where the USA, horrified by the terrible war in Europe, declares that the entire New World is isolated from the old world. No contact is allowed from longitude 30 W to 175 W. Between the massive mine laying efforts and German unrestricted submarine warfare, all transoceanic contact is lost. Little is known of Europe except that the war goes on and on and on. The nations of the New World form a Pan-American Federation that makes great leaps and bounds in technology, and they make vast navies that patrol the longitudes of the boundaries, forbidding all contact. No one is allowed to go "beyond 30".
The story takes place around 2137 AD (I'm guessing from notes in the book). A ship in the PAF navy breaks down and gets blown beyond 30, and drifts to Europe. The Americans find that the continent (and the UK) is a howling Stone Age wilderness. Actually, most of the old world is, except for two empires (Ethiopia and China, both of which exist at about 1920 technology, and both of which are struggling to control Europe). Naturally, the New World makes peaceful contact with the prosperous empire of China, and agree to lift the travel restrictions and bring aid to Europe.
Of course, this scenario is practically ASB, although not exactly magical, so I very hesitantly put it here. I imagine that most of you will tell me that it's impossible (and I agree), but let's make it happen. What would it take?