Nearly half of students who graduated from Lehigh University, Princeton University and the University of Southern California this year did so with cum laude, magna cum laude or summa cum laude honors, or their equivalents. At Harvard and Johns Hopkins, more got the designations than didn’t.

Anyone with a grade-point average of at least 3.4 is granted Latin honors at Middlebury College; the number of students graduating with honors has been rising in recent years, the school says, and was north of 50% this spring.

“I’d...