How to Block Your Number

US-centric: If you want to block your cell phone number from showing up on other phones (for whatever reason), you can do it temporarily simply by dialing *67 before the number you’re calling. According to tech how-to site How To Do Things, you won’t have any way to tell this is working (it does), but if you want to reassure yourself just call another phone number that has caller ID to double-check that your number, indeed, is blocked.
AU – To block your number being call-ID’d in Australia, I believe you need to dial 1831 before the number.