Understanding the Liturgical Worship Service: Acts of Exit

Benediction

Historically: Like the Nunc Dimittis, this was not originally in the Mass, but added by Martin Luther, replacing the Ite Missa est (basically meaning, "y'all can go, now, the mass is over")

Explanation: This is the Aaronic blessing, the one which YHWH commanded Moses to give to the people, to put "My Name on them". Just as we began the Divine Service in His Name, so we end in His Name.

Sacramental: God puts His Name on us.

Scripture: Numbers 6:24-26

Alternatives: How 'bout this one?

Hymns: May the Grace of Christ Our Savior

Postlude

Explanation: While the prelude was about music for meditation, the postlude is more about getting folks excited about the Gospel they have just heard. Unfortunately, this also gives rise to that when you go into church, you hear sad music, but when you leave, it's happy music. Some organists combat this by playing fiery renditions of hymns sung during the service.
Alternatives: For Good Friday (and some congregations add Maundy Thursday), there is no postlude, but instead everyone leaves in silence.