In cursive or fancy script, what is the thing that connotes an underscoring of the text above (such as a name written on the envelope of a card) or that marks the end of a written passage (such as a diary entry) that looks like a giant tilde (~) with two forward slashes (//) through it?

The closest thing I can find in the Unicode character set is the “swung dash”, hex code 2053. I don’t know if this is exactly the same character as the one you mention—the only place I see that character explicitly is in the Zapfino font. A google search for “swung dash” doesn’t come up with much information, but does give hints that the mark you’re asking about might be a different entirely. If that’s in the Unicode set, I can’t find it.

I don’t know if this decorative piece has an additional name. It may just be a flourish.

I know what you’re talking about but I do not know it’s name. I’d assume that it has a name because it shows up a lot.

@jeffporten, from my understanding, the only difference between a tilde and a swung dash is it’s location on the line. A tilde ~ is in the middle of the line, where as a swung dash is at the top. (think of _ and – )

Add a few little hearts and it is Penn. Dutch art. Swung dash comes right after “Honor your partners, honor your corners.”

@Perchik—I don’t think so. The swung dash is used to replace a missing word, and when I’ve seen that in period texts, it is far larger than a tilde; it’s closer to being one or two em-dashes in length. If you pull up the swung dash and the tilde consecutively in the Unicode character browser in OS X (show contents of /System/Library/Components/CharacterPalette.component, then navigate to Contents/SharedSupport/CharPaletteServer.app; the search box is bottom middle), the swung dash is larger by a factor of about 60%.

In typography, I usually see these referred to as “ornaments,” but I don’t think I’ve ever seen a specific name for any of them.