LaTeX users may know about Detexify, a website that lets you draw a character then looks up its TeX command. Now there’s a new site Shapecatcher that does the same thing for Unicode. According to the site, “Currently, there are 10,007 Unicode character glyphs in the database.” It does not yet support Chinese, Japanese, or Korean.
For example, I drew a treble clef on the page:
The site came back with a list of possible matches, and the first one was what I was hoping for:
Interestingly, the sixth possible match on the list was a symbol for contour integration:
Notice the treble clef response has a funny little box on the right side. That’s because my browser did not have a glyph to display that Unicode character. The browser did have a glyph for the contour integration symbol and displayed it.
Another Unicode resource I recommend is this Unicode Codepoint Chart. It is organized by code point value, in blocks of 256. If you were looking for the contour integration symbol above, for example, you could click on a link “U+2200 to U+22FF: Mathematical Operators” and see a grid of 256 symbols and click on the one you’re looking for. This site gives more detail about each character than does Shapecatcher. So you might use Shapecatcher to find where to start looking, then go to the Unicode Codepoint Chart to find related symbols or more details.