Kitty has a built-in emoji picker which you can use to search for and select an emoji character to be placed in your current terminal context. This is handy because Mac OSX's built-in emoji picker (Ctrl-Cmd-Space) doesn't work in Kitty.
To open up Kitty's emoji picker, hit Ctrl-Shift-u (or prefix u with
whatever your Kitty metakey is). You'll see a full screen menu with 4 different
tabs. If you move to the Emoji (F2) tab (Ctrl-] and Ctrl-[ to navigate),
you'll be able to search for an emoji based on its metadata name.
For instance, if I type check, I'll see a bunch of unicode characters that
match that term including 3 ✅ White heavy check mark. By hitting tab until
I reach that result, I can hit Enter to send that emoji to the terminal
context.