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DISCLAIMER: This only applies to the case of those who died in infancy. In no way does this imply universalist soteriology. Remember that God in His sovereignty has an appointed time for the salvation of every individual believer (Acts 13:48) - and that includes the infants. 

How does God redeem those who were stillborn, were miscarriaged, or died in infancy? Before we could answer this question, I think more appropriate questions should be asked first.
 
First question to be asked is "Why does the soul of man need salvation?" Because the Bible says man is a sinner (Romans 3:9-18, Ephesians 2:1-3). And because God his Creator is a perfectly just and spotlessly holy God, man deserves condemnation. Sin, no matter how small it might seem to our own eyes, is too great a deal to be ignored simply because it is a direct offense to God Himself; therefore, it is rightly that everyone who sins should be penalized in God's holy court. The bad news is that all have sinned and therefore, everyone deserves to be punished. The good news is that God has already provided the remedy through Christ.
 
The second question is "How can a soul be saved?" The Bible says that it is by grace through faith in Christ that a man is saved (Romans 3:22-26, Ephesians 2:4-9). It is essential to know that is the grace of God that brings salvation to sinners. Apart from His grace, man is utterly hopeless when it comes to salvation.  But because of His grace through Christ's atonement that legally pardons the sin of man and through the Holy Spirit's work that convicts sinners to repentance, salvation of man became possible.
 
The third question is "Does infants need salvation?" The quick answer to that is "Yes" which leads us to the fourth question: "Why?" It is because the Bible says all have fallen short of the glory of God (Romans 3:23) - and that includes the infants. In Psalm 51:5, David confessed, "I was brought forth in iniquity, and in sin my mother conceived me." Since the fall of Adam, everyone who is born of him has inherited his sinfulness (Romans 6:12-14). This leads us to the fifth question: "How does salvation by grace through faith in Christ apply in the case of the stillborn, miscarriaged, or infants who died in infancy?"
 
First of all, we should recognized that the grace of God for the infants has been declared in the Scriptures. We can read in the Gospels that Jesus declared the kingdom of God to be the inheritance of little children (Matthew 19:14; Mark 10:14; Luke 18:16). Secondly, Scriptures tells us that infants do have an inborn faith (Psalm 8:2, Matthew 21:16; Mark 10:15). Lastly, it is implicit in the Scriptures that the atonement of Christ is applicable to them. John 3:16 says, "For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish, but have eternal life." Since infants do have an inborn faith, it is safe to imply that they belong to the category of those "who believe."

All Scripture quotations are from The Holy Bible, Modern English Version. Copyright © 2014 by Military Bible Association, published and distributed by Charisma House. Used by permission. All rights reserved.