European leaders followed a careful playbook when President Trump visited Scotland over the past five days.

They pushed, but delicately and only so much, toward greater involvement in causes important to Europe. They flattered. And, above all, they avoided criticizing him in public.

Using that strategy, developed over months of trial and error, European leaders engaged in a delicate push-and-pull with Mr. Trump, who had threatened to abandon Ukraine and NATO and to shut off American markets from Europe, claiming the European Union was “formed in order to screw the United States.”

And they had some success. E.U. leaders agreed to a trade deal that many view as giving Mr. Trump too much and that the French see as a major retreat, but they were able to nudge the American president into dropping his most severe tariff threats. They were also able to coax changes from Mr. Trump, at least for the moment, on issues they consider crucial. They cajoled him into a pledge of more aid for the starving children of Gaza and induced him to take a more aggressive stance toward President Vladimir V. Putin of Russia, which included cutting down the time Mr. Trump had allowed the Russian leader to end his invasion of Ukraine.

The Scotland meetings, held at Mr. Trump’s golf courses, capped off a surprising run in recent weeks in which European leaders have persuaded Mr. Trump to both embrace military support for Ukraine and to remain involved in NATO, after other countries increased their financial contributions.