It's called Character Map in Windows, and displays all the characters in any selected font.
It's a "System Accessory" so you can select any character, copy it and paste into any compatible program. Alternatively you can select a list of individual characters, copy the selection box, and paste them into your other program, and then cut-n-paste them to the appropriate places. The only minor annoyance is that the pasted chars don't often match the font size you're using in the document so you may have to resize.
When you click or hover on a char in Character Map, side boxes also show you the Decimal character value if it's an ASCII char so that you can use the Alt-NumPad method of entry, and will show you the Unicode HEX value if you tell it to show Unicode. Either the decimal or hex values can be used to code the correct chars into an html post, but in Windows the chars pasted into a post generally look okay at least to other Windows users, as long as you stick to Latin based fonts.
Windows Word also has numerous "shortcut" key combinations that allow you to enter valid characters - especially for alternate languages. The advantage of the shortcuts is that once you know them for the chars you use you can enter them "at typing speed" without having to go to another source.
Another handy feature is that in Word you can put you cursor next to an unknown character and hit Alt-X to toggle it to display the Unicode Hex value. This usually works even if the character displays as an "unknown" if it's due to your using a font that lacks that char.
I'd presume that Mac Word probably works the same but with cuter names for the buttons.