Because Harry Potter did not attend Hogwarts for his seventh and final year, he did not take the N.E.W.T.s, which are the exams young wizards about to graduate must take before finishing school. J.K. Rowling, author of the Harry Potter novels, has given no indication that Harry ever returned to Hogwarts to finish his final year, though she has said that Hermione Granger did so.
In "Harry Potter and the Deathly Hallows," the seventh book in the Harry Potter series, Harry does not return to Hogwarts for his final year of schooling, instead choosing to embark on a quest to destroy Voldemort's Horcruxes. Ron Weasley and Hermione also leave school to join Harry on this mission. Because they are not at school, they are not able to take their N.E.W.T.s., and it isn't clear whether the N.E.W.T.s were even administered that year.
N.E.W.T.s stands for Nastily Exhausting Wizarding Tests. Each seventh-year student at Hogwarts must take one of these examinations for every class. The Wizarding Examinations Authority of the Ministry of Magic supervises these tests. Although no N.E.W.T. test taking is ever portrayed in the books or movies, the administration of the N.E.W.T.s is similar to that of the O.W.L.s, or Ordinary Wizarding Levels, given at the end of the students' fifth year at Hogwarts.