An amniocentesis can also be done during the third trimester of the pregnancy to determine if the baby's lungs are mature enough for delivery, or to evaluate the amniotic fluid for infection. 1 | 2 | 3.ecause amniocentesis presents a small risk for both the mother and her baby, the prenatal test is generally offered to women who have a significant risk for genetic diseases, including those who: 1  Have an abnormal ultrasound.