crt

On a PC CRT monitor, the best way to get flawless 240p is to use an ultrawide resolution and scale output to fit that. If you use a very large horizontal resolution, your monitor's dot pitch will hide any scaling errors from non-integer scale factors, meaning you can use one output resolution for all games that output 240p at different horizontal resolution. This is especially useful for PlayStation games that can change output resolution on the fly, so setting an unscaled resolution will be impossible there without automatic mode changing. It will also let you use blur shaders more effectively if you want blending effects.

I use RetroArch on Windows for most of my emulation, so when I want to use one of these modes, I set the following in my config files:
video_fullscreen_x
video_fullscreen_y
video_aspect_ratio (set to 60.000 most of the time)
video_refresh_rate (set to x / y)
video_fullscreen = "true"
video_windowed_fullscreen = "false"

The last one is important so RetroArch won't just use your desktop resolution instead of your custom resolution. Before using the video mode, it has to be set in your video driver using your video driver's custom resolution function (or using ToastyX's Custom Resolution Utility to create an EDID override).

Some of the video modes I use on my 17-inch Dell dot mask CRT monitor:

3840x240 @120hz
video_aspect_ratio = "16"
This one doubles the refresh rate to compensate for the low resolution to keep the horizontal refresh at 31khz. You will need to either use frame doubling or black frame insertion on this one or else you get motion jitter. Set the follwing in your config file:
video_black_frame_insertion = "true"
or
video_swap_interval = "2"
but not both or it will run half speed. Black frame insertion will have smoother motion but will be half as bright, while frame doubling will be fully bright but will have double imaging on scrolling images. Unfortunately, this won't handle games that run in interlaced mode without downscaling them. For those I take a different approach.

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3840x480 @60hz
video_aspect_ratio = "8"
This one will display 240p games with line doubling by default, but you can use 100% black scanlines to eliminate the extra scanlines. The image should be the same as it is using 240p 120hz with black frame insertion, with some very minor differences. You can use a scanline shader get the black scanlines, but if you want interlacing you'll need the CRT-Geom shader to do that. I've put together a modified CRT-Geom that will do this for 480p: http://www.mediafire.com/download/01bahm4mza1w3ar/interlacing_scanlines.7z When I use this, I get proper interlacing on 480i content (such as Tekken 3 on Playstation) and proper scanlines on 240p content, with seamless switching between the two (needed for several Playstation games such as Chrono Cross to look correct).

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I sometimes use other modes for arcade games in MAME that run at different refresh rates (i.e setting 640x480p 57.551hz for DoDonPachi), and you can use the same ultawide resolutions on them if you have games that use different horizontal resolutions but the same refresh rate.