How to mock persisting and Entity with Mockito and jUnit

You could use a Mockito Answer for this.

doAnswer(new Answer<Object>(){
     @Override
     public Object answer(InvocationOnMock invocation){
        Article article = (Article) invocation.getArguments()[0];
        article.setId(1L);
        return null;
     }
  }).when(em).persist(any(Article.class));

This tells Mockito that when the persist method is called, the first argument should have its setId method invoked.

But if you do this, I don't understand what the purpose of the test would be. You'd really just be testing that the Mockito Answer mechanism works, not that the code of Article or of EntityManager works correctly.

public class AssignIdToArticleAnswer implements Answer<Void> {

    private final Long id;

    public AssignIdToArticleAnswer(Long id) {
        this.id = id;
    }

    @Override
    public Void answer(InvocationOnMock invocation) throws Throwable {
        Article article = (Article) invocation.getArguments()[0];
        article.setId(id);
        return null;
    }
}

And then

doAnswer(new AssignIdToArticleAnswer(1L)).when(em).persist(any(Article.class));