First it is important to understand that "righteous" does not mean "sinless." There are several people in Scripture who were definitely sinners and were still considered righteous by God. [Abel (Heb. 11:4), Noah (Gen. 6:9), Abraham (James 2:23), Cornelius (Acts 10:22), David (1 Sam. 24:17)] We can look at this list of men who were used by God in great and mighty ways and see that at times they had some very significant sin issues. This is a testimony to God's grace.
A woman who desires to live a righteous life will obey the commands of Scripture and adhere to what the Lord teaches. This does not mean we become women who perform righteous acts to be seen as righteous. There is to be a desire at the heart level to honor the vows you make, speak truthfully to others, not murder in your heart in anger, not hate others, be content in your circumstances, and abhor idols. These are some of the actions of righteous people. Unless these things come from a desire to honor and glorify God by how you live your life, then there is no spiritual value in doing them. You become like the Pharisee who as he prayed to God thanked God that he was more righteous than the "sinner" next to him (Luke 18:9-14).
People who are righteous very often have difficult and troubled lives. It is a mistake to think that people who have sorrows and hardship are suffering because God is "punishing" them. To do so makes you like Job's 3 friends! Christians are warned that there is trouble and tribulation for us in this world, we should expect suffering because we are supposed to be counter-cultural. Our priorities and our values are to be different from those of our fellow man which is going to cause us problems. We can be trial magnets, which is why we are to keep our focus heavenward and our eyes fixed on Jesus.
Righteous women are praying women. There are some women who have been praying for years for a specific thing, and their prayer has gone unanswered. Such was the case with Hannah (1 Sam. 1) who prayed for a child, and Sari (Gen. 16:1-2) and Elizabeth (Luke 1:5-17) who were also barren. All of these women beseeched the Lord to give them children. They were faithful to continue to pray beyond the time that anyone would consider reasonable. They petitioned the Lord to remove their shame and the cultural disgrace of childlessness.
You may know how the story unfolded for these women; they all became mothers, 2 of them well advanced in years! This brings up the next point, God answers the prayers of the righteous! Even though it may take many months or years, God is faithful to remember our petitions and to answer us. We are to remain faithful in prayer and continue to believe that God will answer.
O You who hear prayer,To You all men come. Psalm 65:2 (NASB)
Part of our problem is that we don't always like the answers we get to prayer. Our idea of God being faithful in answering our prayers is to give us what we want. We choose not to look at His goodness in not giving us everything we ask for. God is all-knowing (omniscient) and will always do what is best for us and brings Himself glory. He always does that which is honorable and right and will be the most effective at conforming us to the image and likeness of Christ.
Other times, the answers to prayer we get are better than we ever could have imagined! Hannah had that experience when she gave birth to Samuel, and Elizabeth did as well when she gave birth to John the Baptist. Sarai's son Issac became the father of Jacob through whom the 12 Tribes of Israel came leading down through the ages to the birth of our Savior Jesus Christ.
Each of these women who prayed so faithfully had their prayers answered in God's timing, and in God's way.
He who is the blessed and only Sovereign, the King of kings and Lord of lords, 1 Timothy 6:15b