It is this meeting that we celebrate today.
FIRST READING: Zephaniah 3:14-18a
(Rejoice, for the LORD prepares to restore and bless His people.)
(Praise the LORD, who lifts up the needy, and makes the barren a joyful mother.)
or CANTICLE 9 (FIRST SONG OF ISAIAH): Isaiah 12:2-6 ("Sing the praises of the LORD, for He has done great things.")
EPISTLE: Colossians 3:12-17
(Abound in love, and forgiveness, and peace, and joy, and singing.)
THE HOLY GOSPEL: Luke 1:39-49 (or 1:39-56)
(Mary goes to visit Elizabeth. The two women greet each other with hymns of joy, and the infant John stirs in the womb as if to participate.)
PRAYER (contemporary language)
Father in heaven, by whose grace the virgin mother of your incarnate Son was blessed in bearing him, but still more blessed in keeping your word: Grant us who honor the exaltation of her lowliness to follow the example of her devotion to your will; through Jesus Christ our Lord, who lives and reigns with you and the Holy Spirit, one God, for ever and ever.
Interested in a special devotion for today? Why not try praying the rosary? I know... "Protestants don't do that!" Well, the first successful Protestant, Martin Luther, would disagree with you:
"Our prayer should include the Mother of God . . . What the Hail Mary says is that all glory should be given to God, using these words: "Hail Mary, full of grace. The Lord is with thee; blessed art thou among women and blessed is the fruit of thy womb, Jesus Christ. Amen!" You see that these words are not concerned with prayer but purely with giving praise and honor . . . We can use the Hail Mary as a meditation in which we recite what grace God has given her. Second, we should add a wish that everyone may know and respect her " (Personal Prayer Book, 1522).
A slew of others (like Calvin, Zwingli, and Wesley) had other important things to say about the Blessed Virgin Mary - so don't be scared to at least explore what Christians have believed about her (so long as we do not require more than Scripture demands, nor say something Scripture proscribes). See if it's at least as biblical as your normal prayers!
The "Hail Mary" written above has the scriptural references after each line. Some Evangelicals feel that it is blasphemous to say that Mary is "Holy." But Peter said "You shall be holy because I am holy’" (1 Peter 1:14-16). I don't think Evangelicals would think that is blasphemous. Mary's obedience to God and closeness to Jesus made her holy. Our nearness to Jesus makes us Holy.
There is a inscription found in the grotto of the The Basilica of the Annunciation in Nazareth, which reads "Ch-e Maria," which is an abbreviation of the Greek phrase "Chaire Maria" or "Hail Mary." This was left between 200-300AD by a Greek Christian who visited the site of the Annunciation, as presented in Luke 1:28. (You can see it here.)
What is of special significance here is that "Chaire Maria" ("Hail Mary") is not the specific greeting in Luke's account. Rather, Luke records Gabriel as saying "Chaire Kecharitomenae" or "Hail, Full of Grace" (or "Hail, Perfectly Graced"). But, this is not what the inscription reads. Rather, it addresses Mary by name, showing that this early Christian had a personal devotion to her; and it is also the very earliest record of the Catholic prayer, the "Hail Mary."
One should also note that the "Holy Mary, Mother of God, pray for us sinners now and at the hour of our death. Amen." was not normally added until after the Council of Trent - thus it is not part of the unbroken tradition of the Latin Rite. Neither is the Salve Regina prayed at the end - so if your conscience is troubled by these Marian devotions just leave them off. The rosary can still be a very effective tool of prayer.
The Anglican Service Book also provides an alternative form to end the Angelus:
V. Hail Mary, full of grace, the Lord is with thee: blessed art thou among women, and blessed is the fruit of thy womb, Jesus.
R. Son of Mary, Son of the living God, have mercy upon us, now and at the hour of our death. Amen.
(For a good Roman apologetic of the rosary, go here. However, I cannot endorse everything they say.))