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Donald J. Trump is going to spend his time in the coming weeks before the Republican Party’s nominating convention in July considering a running mate, musing potential Supreme Court picks — and, possibly, heading to Scotland for a ribbon-cutting.

Mr. Trump is considering whether to travel to Scotland in June for the unveiling of the renovated Trump Turnberry, a famous golf course that he acquired in 2014 and which has hosted championships.

“We just did a massive renovation of the whole place,” Mr. Trump said in an interview this week. “We’re having an opening in June, and the question is, will I fly over, cut the ribbon and fly right back, or not.”

Such a trip could have advantages, particularly if Mr. Trump was able to schedule meetings with European officials to add a presidential patina.

But it would also take him off the campaign trail in a heated battle over the economy and jobs.

Such foreign trips taken by presidential nominees, if they include ceremonial stops and meetings, can be fraught with peril. Mitt Romney’s trip to Europe in 2012 was pockmarked with troublesome encounters and negative headlines. So was a trip taken by Gov. Chris Christie of New Jersey in late 2014.

