Dan argues that Europe does this pretty well, pointing at the Czech/Slovak divorce, Montenegro's peaceful referendum/secession, and now Scotland's referendum process. To be clear, Europe had nothing to do with the first one, as the Czechs and Slovaks agreed to disagree and go their separate ways precisely at the same time that Europe was not being all that helpful/sucessful managing the secessionist/irredentist/boundary changing crises of Yugoslavia.
People forget but the EU in its first few days of EU-ness (having recently transitioned from EEC) tried to manage the Yugoslav crisis. They sent "ice cream men"--observers in white uniforms--to serve as monitors, and they were utterly irrelevant. They thought that recognizing the more fit units as states might reduce the violence. Not only did this hope lack much logic, but the EU violated their own rules. The Badinter Commission was given the job of recommending which parts of Yugoslavia should be recognized, based on a variety of criteria, and the commission chose Slovenia and Macedonia. The EU chose then to recognize Slovenia and Croatia--because Croatia had Germany as a friend and Macedonia had Greece as an un-friend.
To be fair, the secession of Montenegro reflected much lessons learned, with the EU serving as a key player pushing for a reasonable process including a 55% majority required qualify for independence. Note that the Scottish referendum is not being managed by the EU, and as far as I can tell, is still going by 50% plus one (which I cannot stand--a very narrow and potentially temporary basis of support).
Dan ignores the other violent cases that have petered out--Northern Ireland and the Basques. Which is fine, since they are less violent now. But again, Europe has little to do with it. What does? That magic sauce of democracy and economic development. Canada's own secessionist movement--Quebec--has been similarly non-violent except for a quite token murder in 1970.
How does this work? Jason Sorens has written much on this, but the basic idea is that if you give people a chance to leave peacefully, via democratic means, they do not need to choose violence, and they then often do not choose to leave. The benefits of leaving an advanced democracy with a good economy are not so great. The costs are always downplayed but are quite real.
Both violence and secession are far more popular where people do not have the means to address their grievances through the political system--so they opt out. What makes Europe different is not the EU but the prevalence of strong democracies and decent economies (even now, when compared to elsewhere).
So, I would focus less on Europe and more on the stuff that has spread--democracy--and on the economics that create incentives/disincentives.
Still, Dan is right that we can think about Europe as a model for peaceful boundary change--but it is less about EUROPE and more about the characteristics of European countries. And, yes, blaming Europe for messing up the boundaries of the rest of the world is fair game.*
* Although to be fair, the Europeans drew many, many boundaries and irredentism is rather rare.