Constitutional law is my forte, but this is a good question. I think that there is a lot of overlap between what the 9th amendment protects and how the Court interprets substantive due process. In fact, I cannot recall which justice, but in Griswold, the Court agreed that married women have a right to contraception. But, the Court could not get a majority opinion on how it reached that conclusion, with the Justices debating whether the 9th Amendment or the Due Process clause of the 14th amendment supported the right to contraception.
And, for what it is worth, Kennedy is a Due Process guy. I cannot recall a decision in which he relied on the 9th Amendment, albeit that does not mean that one does not exist. Of course, for preferring to analyze the situation under Due Process, Kennedy has never done a good job of distinguishing Equal Protection from Due Process. But, that is another issue.
Finally, for what it is worth, Substantive Due Process refers to a doctrine in Constitutional law. The 14th Amendment states that people may not be deprived of liberty without Due Process. Starting in the early 1900's, the Court interpreted this to strike economic regulations, reasoning that people were being deprived of liberty without due process of law. In Carolene products, and the infamous footnote 4, the Court reversed ground and decided that it would use Due Process to protect distinct and insular minorities, giving rise to the Substantive Due Process Doctrine. In contrast, procedural due process refers the rules of the court. A person cannot be sent to jail with procedural safeguards: notice, a trial, the right to jury, appeal, and attorney, etc. Substantive Due Process refers to a set of rights so fundamental to our society and liberty that even with the proper safeguards, the government is not justified in depriving us those rights.
