Let's get one thing straight. Please don't call babies "the unborn." Please call them babies or children. The USCCB usually uses the term "unborn children." If you must make a qualification, then refer to "unborn children" as they do—but only if such a qualification is truly necessary. But I sincerely think speaking about babies and children without qualification is better. I have several reasons:

1. Calling children "the unborn" is objectifying and essentializing. It may be literally accurate, but it diminishes the totality of the person to whom the term is applied. (For analogous reasons, it is commonly regarded as impolite—and in certain cases even derogatory—to refer to persons as "the handicapped." The fact that the children themselves are too young to be personally offended is beside the point.)
2. Those who are disinclined to regard children in the womb as human persons may find in the term "the unborn" a convenient euphemism. By not referring to persons but only to some feature about them, the term may help some psychologically avoid the question of whether unborn children are really even persons "in a full sense" or "at all." Don't cede that ground!
   • Instead, consider referring to "children after they are born" or "born children" where social convention would suggest that such qualification is superfluous. By adding it, you imply that it makes a meaningful distinction: namely, that "children before they are born" is not a nonsense phrase, and that the specific children being referred to were already children before they were born. 
3. Calling children "the unborn" may also tend to concede a key pro-abortion assumption, namely that one could responsibly discern and define watershed events in the life of a mother and child in relation to which one could justify abortion. Again, don't cede that ground, not even implicitly!
   • Instead, draw out the implicit assumptions. The presumed importance of watershed moments for justifying abortion hinges on further assumptions about the cogency of the concept of "viability"—the (purported) ability of the child to "survive" outside of the womb and the (putative) non-personhood of a child who could not "survive" outside the womb.

Even more than "born" and "unborn," "survival" are "viability" are mere question-begging distractions. Don't be deceived. My son Dominic, at the ripe old age of 4, is still not "viable." He wouldn't last very long at all if his mother and I didn't care for him constantly and intensively. To be frank, some adults I've met aren't "viable" yet! Even the very self-sufficient Bear Grills needs a minimally hospitable environment in which to ply his bushcraft. Likewise, children (born or yet to be born) and adults need an appropriately hospitable environment in which their natural tendencies toward growth and maturity can occur.

Christians hinder our advocacy, to the detriment of the children for whom we would be advocates, when we allow the "birth event" to be too prominent in our thinking. The birth of a child is, undoubtedly, an important event in the life of a family and of the child being born. But there is an even more important continuity between the womb and the world. When it comes to the protection and nurture of children, whether they are born or not yet born is a red herring. What's most important is that they are people, like you and me. Let's remember to talk about them as such.

Reading (Lk 1:38-40)
Mary said, “Behold, I am the handmaid of the Lord. May it be done to me according to your word.” Then the angel departed from her. During those days Mary set out and traveled to the hill country in haste to a town of Judah, where she entered the house of Zechariah and greeted Elizabeth.
V/. For the Lord has looked with favor on his lowly servant,
R/. from this day all generations will call me blessed. 

Prayer
Lord Jesus Christ,
Your mother was obedient to the Divine will
amid trembling and awe.
Through her intercession, we pray You,
look kindly on all expectant mothers.
May any trials they now endure yield in the joy of new life.
For You live and reign with the Father in the unity of the Holy Spirit,
God, for ever and ever.
Amen.