Search for your ancestors and relatives who were married in New Jersey. This is an enormous aid to adoptees whose birth parents were married but for whom you have the last name of just one party. And if the adoptee was born in New York City, the given surname may be the mother’s husband’s name, and from that you could possibly identify her in the New Jersey marriage records. Then you can add those names to your family tree, including marriages that occurred after the 1940 Census.
These are sets of images of the index, not a text-searchable database. That’s in development. Each index covers a year and is alphabetical by groom or bride last name. The groom index is not available for some of the years, but once the indexes are transcribed you’ll be able to search by all names – first and last of each spouse. Reclaim the Records secured these from the New Jersey Department of Health (not without initial resistance from the agency) and made them available for free at the Internet Archive. You’ll want to read the account of what data is available and how Reclaim the Records was able to obtain the massive New Jersey marriage index covering so many years.