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?
CtrlSpace 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 CmdShiftSpace (and, if you disable Spotlight's use of it, CmdSpace) 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 4 digit hex code; on releasing Option it should be typed. You could stay in that mode as long as you don't need any characters beyond
In many CLI/TUI applications you can press CtrlV in order to tell the application to accept the next keypress as raw character codes instead of invoking its normal function.