The Supreme Court here in Roe v. Wade used the compelling interest test.
To put it simply the compelling interest test is used by the court, federal or state, to check the if the law is constitutionally valid. In the Roe v. Wade case the Supreme Court had to see if the right to privacy of the 14th Amendment is applied to abortion and they decided it did. They used the compelling interest test to balance this with the state's interest in the welfare of women and the potential human life that is the baby. So the court limited state's regulations on abortion.