When you do something contemplatively, you do it while thinking in a quiet, serious way, not in a hurry. You might sit contemplatively by a window, or look contemplatively at a painting: the body is still, but the mind is working slowly and carefully. It is a formal word, a little like something from a book. In everyday talk people more often say thoughtfully, quietly, or they just say she sat and thought. Though actually it is a bit stronger than thoughtfully. Contemplatively suggests you have gone inside your own thoughts, almost as if you were watching them. You will meet it in novels and careful writing, not in a quick message to a friend.