If you think you may be doing this often enough to buy tools, instead of a large screwdriver, there are actual small screwdriver sized pry tools. They have the advantage of a bend for prying as well as a tip more suitable. Less likely to do damage with those, and they're not expensive.
I usually pry (very carefully) a little to push the pistons back a little (if they're the kind that actually do push back in, some are screw in...) and then use a rubber mallet to beat the caliper past the lip. Note that there's a spec for replacing rotors based on thickness. A rotor with any wear to speak of will obviously have a lip, but the if the lip is really bad, you're probably past the rotor service limits anyways. Easily checked with a micrometer, but they're a bit pricy to buy and aren't commonly available for borrow/rent.