Meditation from Thais is probably one of the first melodies that comes to my mind when I think of musical serenity and poignancy. I first learned it when an elderly gentleman who had played violin all his life asked me to accompany him for a performance of it. While his fingers had grown shakier with advancing years, the experience forever solidified this piece as one of the most beautiful violin pieces I have ever heard.
Massenet composed this instrumental piece as part of his opera Thais. It is of course originally for violin and orchestra, but assuming you aren't hiring a live orchestra for your wedding ceremony, it has been arranged for violin and piano as well. It can also be played by violin and harp, which would be beautiful also. I love Itzak Perlman's rendition of it, and you can find other great violinists who have recorded it also - Joshua Bell, Anne-Sophie Mutter and even my favorite cellist Yo Yo Ma. James Galway (flautist) has also made a recording of it, though personally I prefer the violin version as he has made several adjustments to make it possible on a flute.