The classical punctuation to denote emphasis is the exclamation mark.
However, that applies to the whole sentence. It is sometimes possible to draw a word to the end of a sentence to emphasize it instead of the whole sentence:
I love kittens … not!
Or if the word in question is an interjection, put it between dashes:
The dessert – delicious! – had just 200 calories.
Another alternative I have sometimes seen is putting the exclamation mark into parentheses behind the word.
This is the only (!) way of using emphasis.
But in general, emphasis of single words is achieved via formatting, not punctuation.
Historically, this has been italics, or, since, italics are hard to emulate in handwriting, underlining in handwritten documents. With the advent of typewriters, the underlining convention was reused but on computer terminals, underlining no longer works because you cannot shift the carriage position back in a text document (which is how underlining was achieved on typewriters).
This is probably when people began to hint at emphasis by prefixing and affixing a word with underscores:
In newsgroups, many people switched to slashes,
/like this/. I have no idea where the asterisks come from though.