Broken scope base screw

[Killroy]

That one looks like there's enough head left to saw a slot in it. I'd slit the top, hit it with some heat and get right on top of it with a perfect fitting screw driver and put my weight down and give it a twist. Heat being key.

 

[ELR LVR]

That one looks like there's enough head left to saw a slot in it. I'd slit the top, hit it with some heat and get right on top of it with a perfect fitting screw driver and put my weight down and give it a twist. Heat being key.

Good idea, I have found that also tapping with a punch or something on the offending screw can provide some extra wiggle space in the threads before trying to loosen
Some Kroil or ATF soaked in there while heating should also help

 

[JTEX]

Left handed drills often work well too. Heat then drill in,reverse....lots of times they come right put.