Depending on your editing software.

One way to do it:

Record the source material (the subject being shown on the screen).
Shoot your scene. You can shoot the scene with the monitor/lcd off. While shooting the scene put a piece of green cloth or cardboard the exact width of the screen.

Transfer the source material into editing program. Chroma key and lay it behind the scene. It will burn through and would show clear.

Just my .02

Learn how to do something new everyday!

i might be wrong but the lines going over tv or monitor screens dont have anything to do with fps. It has to do with the shutter speed. If you see the lines, lower the shutter speed and they'll go away, works with my camera.

"Imperfection equals Realism"

I've actually had to do a lot of screen shooting in the past, and I really am opposed to the idea of chroma keying the screens and laying in the footage later, as I think it looks fakey-fake-fake, especially when you're originating on film.

Here are some tips that I have found valuable:

When you're shooting TV screens, make sure your camera's shutter speed is set to 1/60 of a second. There will still be a top-to-bottom scan line, but since CRT TV screens have a refresh rate of 60Hz it's very minimal. Just keep your camera moves very slow and fluid or you run the risk of making the screen look like it is splitting in half.

When you're shooting CRT computer screens, try and use screens that you can set to 60Hz refresh rates and use the method above. Otherwise try and find a refresh rate that corresponds to an available shutter speed on your camera (lots of CRTs are 75Hz, but very few if any cameras feature a 1/75 shutter speed, so this may be difficult)

DLP projectors and big-screen TVs have their own slew of problems, usually manifested in bizarre color strobing. It's best to just avoid these screens whenever possible, maybe unless you're shooting black-and-white.

LCD screens are a thing of beauty and a joy to shoot. No strobing, no scan line issues. You can't really use polarizing filters with them, but that's never come up for me. Whenever possible, shoot from LCD screens unless you're going for a particular CRT-look.

That all applies to video, but much of it also applies to film (everything about shutter speeds, to be sure). But since you're shooting film (and since Bolexes use a 130-degree shutter, you may have some ugly math in your future. Doing the calculation, I see that a Bolex running at 24fps will have a shutter speed of roughly 1/66.5 of a second, so if you want to reduce scan lines on TVs or other 60Hz displays, you should probably shoot at just a touch under 24fps. This would be a problem if you were shooting sync sound, but hey, it's just a Bolex after all. Since Bolexes are governed by inaccurate spring motors, you're probably going to get more scan line problems than you would have with a video camera or crystal sync film camera, but as long as you take issues of screen refresh rate into account (or shoot off of an LCD!) you can significantly reduce your problems.

Good luck!

-----------------
Andrew Gingerich
Exploding Goldfish Films
Check out my blog at http://www.exgfilms.com
and my reel at http://portfolio.exgfilms.com

I had a similar question. Thanks for the ideas!

-Jorge Pinkel