But the crisis has also presented a real conundrum for regional leaders, because it has undermined the attraction of the European Union. In Scotland, for example, there was an assumption that if independent, it would join the bloc without a lot of fuss, since Scots are already citizens of the European Union. (After all, some 20 million East Germans became members of the European Union overnight without even having to whistle the anthem.) But would Scotland inherit the British “opt out” from the euro, or, as a new E.U. state, would it have to commit to the euro? And if so, who would be responsible for bailing out the Bank of Scotland, if it came to that?

As euroskepticism rises in the United Kingdom, these issues have come to bedevil Alex Salmond, the leader of the Scottish National Party, whose slogan is “Scotland in Europe.” The 2014 referendum is supposedly timed to the 700th anniversary of a decisive episode in the first war for Scottish independence, the Battle of Bannockburn.

TRADITIONALLY, the European Union has been popular with the leaders of these regions, said Josef Janning, director of studies at the European Policy Center. “They see strengthening the power of Brussels as diminishing and relativizing national governments, a process accelerated by the single market in Europe,” Mr. Janning said. Many of them have formed regional groupings that bypass the central government — Catalonia, along with Baden-Württemberg in Germany, Rhône-Alpes in France and Lombardy in Italy, for example, are regional powerhouses that call themselves “the four motors for Europe” and together have a bigger G.D.P. than Spain.

“But now,” Mr. Janning went on to say, “comes the crisis,” which presents a dilemma for the regions, because it also means a reconcentration of power by national capitals trying to cut the national budget. “Now eyes are again on Madrid and Rome and Paris and Berlin,” he said, “so regional opportunities are squeezed, and the affluent are made to pay.”

While European leaders believe the answer to the crisis is “more Europe,” which would ordinarily please separatist regions, European voters and taxpayers are shaken, skeptical and angry. Mr. Janning told me: “These regional entities and leaders need to be on the right side of public sentiment and feel close to public opinion and regional identity. So now they’re torn.”

The case of the Basques is a good example. With the defeat of the independence army ETA, which announced the “definitive cessation” of the armed struggle a year ago, the Basques are doing well. They are watching Catalonia and Scotland carefully, but their level of autonomy is already so high, with their own virtual embassies abroad and control over their own taxes, unlike Catalonia, that independence can, to the Basque public, seem destabilizing.

There are also larger anxieties at play, as the frozen world of the cold war slowly melts. For nearly half a century after World War II, until the Soviet collapse, there were few if any border changes in Europe, east or west, with bizarre outcroppings like Transnistria or Kaliningrad, or a divided Berlin paralyzed in amber. The years that followed the fall of the Berlin Wall and the implosion of the Soviet Union were an effort, Ms. Grabbe noted, “to find a new normal.”