My wake up tune is "Chrono Corridor," the original version off of the soundtrack.
There are actually two sorrowful tunes off of the Chrono Trigger soundtrack: "People Who Thre away the Will to Live," which plays just before you leave Arris Dome for Lab 32, and "At the Bottom of Night," which plays during a lot of Glenn's/Frog's flashbacks.
"Crono & Marle," the music box tune, is more nostalgic than sorrowful, if you ask me.
In all honesty, Mitsuda's music box themes are some of my favorites, simply for their nostalgic-sounding qualities. Has anyone heard the music box tune from Xenogears, also titled, "Far Off Promise"? That's even more nostalgic than "Crono & Marle!"