For God is my witness, whom I serve with my spirit in the gospel of his Son, that without ceasing I mention you (ESV)
Have you ever told someone you were struggling with a situation and they responded with an immediate "I will be praying for you," yet you questioned their sincerity. Sometimes when people make a promise to pray it is almost like saying "God bless you" when someone sneezes. People say certain things just to be polite.
The apostle Paul is not lacking in sincerity when he promises to pray. He tells the church at Rome that he mentions them to God in prayer without ceasing. He takes this very seriously. It is more than him trying to break the ice with these people or an attempt to be nice. He says that God is his witness that he is praying for them and says, "whom I serve with my spirit."
Paul took sincerity seriously. Previously he had been a pharisee. The pharisees were the religious leaders of the Jews who lived by such a rigid code of laws that Jesus scolded them for making the law so difficult that not only could they not follow it, but no one else could either. Paul had worked sincerely as a pharisee. He had worked hard with his body, but not his spirit. His spirit was spiritually dead before Christ.
Paul had also seen all of the pagan religions that were so prominent in Greek and Roman culture. Idols abounded in every city. People were sincere in their idolatry. But their spirit was not transformed. Paul has discovered that in his service in the Gospel of Jesus Christ he is finally able to serve with his spirit. His spirit has been changed by God. And when he says he is praying, it is sincere.
Has your spirit been changed by God's mighty Holy Spirit? Do you have a personal relationship with Jesus Christ. If so you are set free to walk a true sincere life before the Lord. Commit yourself today to serving him. It will likely mean serving others.