The best known tune for "Recessional" is an anonymous sixteenth-century German hymn tune called "Old Hundred Twelfth." Words and music appeared in the Episcopal Hymnal 1940. The elegiac tune is perfect for the message.
The hymn was, unfortunately, excised from the Hymnal 1982 on P.C. grounds -- the "lesser breeds without the law" line, of course. I hold by the Hymnal 1940 Companion's comment that "Such criticism of a single line overlooks the devout prayer which follows."
It's Hymn # 147 in the 1940 version, indexed under the first line.