Old Testament Jewish believers believed in the coming Messiah and were saved. Are Jews today who believe the same thing saved? 

I think I see your concern. If Old Testament Jews were saved as they looked in faith toward the arrival and work of the promised Savior, it would seem logical that Jews who today continue to look for the arrival of the Messiah will also be saved.

DO THEY HAVE FAITH?

When talking about modern Judaism and specific Jews, it's always wise to ask if the people have a messianic faith at all. Secular Judaism is pervasive and views Jews as an ethnic, cultural, or political group more than seeing them as a community of faith. Jewish scholar and writer Rabbi Levi Brackman admits, "It is indisputable that a disproportionate amount of secular Jews self identify as atheists or agnostics."

This is not to say that messianic faith is absent from modern Jews. Observant Jews still confess in accordance with "Principle 12" of Rabbi Moses Maimonides' (a.k.a. Rambam) Thirteen Principles of Jewish Faith: "I believe with perfect faith in the coming of the Messiah. How long it takes, I will await His coming every day." But simply to assume this is so among all Jews is unwise.

DO THEY HAVE THE BIBLICAL MESSIANIC FAITH?

The object of one's faith is always more important than simply having a faith. Sadly, most Jews who continue to await a Messiah are not looking for the deliverer as defined by the Old and New Testament. So to answer your question one would have to investigate what kind of "coming Messiah" is anticipated.

The most prevalent hope within modern Judaism is that the Messiah will be a great political and military leader who will successfully wage war for Israel. He will establish an earthly government in Israel both for Jews and Gentiles worldwide. He will rebuild the Jerusalem temple and reestablish the Mosaic covenant worship and court system. But the idea of a divine being who will sacrifice himself to save sinners from the guilt and consequences of their sins is for the most part repudiated by contemporary non-Christian Jewish thought.

No wonder traditional rabbinical Judaism today does not believe that Jesus of Nazareth is the Messiah! Their hope is not in the Messiah promised in the Old Testament but a caricature of the Messiah fashioned from a selective, secularized use of Bible promises.

THEY NEED SAVING FAITH