“I feel sorry for him. I’m disappointed,” Mr. Bösche said. “Political strings held him back from fulfilling his hopes and ours, maybe. It’s become more clear to us now in the U.S. presidential campaign.”

Mr. Obama, he said, “was a golden, golden light — that’s why it’s so sad.”

Mr. Bösche, who was born in Hamburg when the Allies defeated the Nazis in 1945, said: “The Americans made Germany what it is today, with your help. That’s why it’s so disappointing now, that I can’t look up to the U.S. today.”

Of course Mr. Obama made mistakes, those interviewed said, especially in the Middle East and in dealings with his Russian counterpart, Vladimir V. Putin. And many are unhappy that the Guantánamo Bay prison has not been closed, as Mr. Obama had promised.

But they also praise the nuclear deal with Iran, the opening to Cuba and Mr. Obama’s reluctance to go to war. They are looking forward to what is most likely his last visit as president, when he returns to Berlin in mid-November to have one more session with his closest European collaborator, Chancellor Angela Merkel, herself weakened by long tenure and the migrant crisis.

Their views are reflected in opinion polling in 10 European Union countries done in the spring by the Pew Research Center. The polls indicate that Mr. Obama restored more positive feelings among Europeans after the deeply unpopular President Bush.

More than half of the respondents still expressed confidence in Mr. Obama, radically higher approval figures than those for Mr. Bush.

Norbert Röttgen, the chairman of the foreign policy committee of the Bundestag, said that for Europeans, Mr. Obama’s legacy would remain largely positive. He noted in particular the president’s achievements with Iran and Cuba and national health insurance.