To communicate with a serial-type device over a Telnet socket, I need to type the null character (ASCII 0) and all other non-printable ASCII characters.
On Windows, you hold Alt and type the ASCII code.
How do I do this on Mac OS X?
Ctrl + Space sends ASCII NUL.
For the general case, System Preferences → Keyboard → Input Sources, scroll down the list and select Unicode Hex Input.

You can then use Cmd + Shift + Space (and, if you disable Spotlight's use of it, Cmd + Space) to switch between input modes or assign it a keyboard shortcut of its own (and presumably another to switch back) in System Preferences → Keyboard → Keyboard Shortcuts.
Once Unicode Hex Input is enabled, you hold down Option and type the four-digit hexadecimal code; on releasing Option it should be typed. You could stay in that mode as long as you don't need any characters beyond U+007F (or of course type them all with hex input instead of, say, Option + e, e to type é).
In many CLI/TUI applications you can press Ctrl + V in order to tell the application to accept the next keypress as raw character codes instead of invoking its normal function.