Script typefaces that mimic the cursive writing of the 17th and 18th century called formal scripts. These fonts feel very storybook-esque, and traditionally were created with the use of a writing quill or a metal nib pen, much like those used to create calligraphy.
These fonts have been revived and are primarily used for formal occasions such as wedding invitations, anniversary cards, diplomas, and invitations to black-tie affairs. These are thought to be the most elegant and sophisticated typefaces available. Their inherent downside is that sometimes they are so elaborate that they become hard to read when using a lot of text.
If you're going to use a formal script font or typeface, keep it simple. Don't type a large paragraph of text with a script font - instead use it for important things such as names of events or people being honored. If you're going to use a formal script font, it's worth using it at a larger size to increase how easily it can be read.
In the example here, you can see Scarlet, a typeface collection that has a very classic script feel to it. Here are two places where you can download a similar font: http://fontzone.net/font-details/Scarlet/, and http://www.azfonts.net/load_font/scarlet.html.