If its a computer monitor CRT, then there is little that can be done. These have too high of a dot pitch, to make the image look decent.
They do sell a small device, I believe its called a Scanline Generator. It does help a little with the look... but its still artificial.. and not correct to the way the older machines looked.
If its an older crt tv, you have a better chance. The older the model, the more true to the look.
Composite is a little too distorted.
Svideo - while can have some color issues, can look quite good.
Component - has the cleanest picture and no issues with oversaturated reds.. But, it can look almost as clean as a PC Monitor.
The older the TV, the larger the Shadowmask is. This greatly effects the light leaking, color blending, and other effects that old arcade monitors presented. As TVs changed, the shadowmask size changed. Dot-Pitch got smaller. Light no longer leaked, so there was none of the color blending that used to happen. (I think this may also have happened in the arcade industry, to even its low res monitors, making it hard to know what games really used to look like when they were factory new)
Also, Arcade monitors tended to get slightly out of whack quite quickly. There are internal adjustments on arcade monitors, and probably the same on most TVs. There is voltage & focus dials that are located on the main juice-box of the monitor board. (Warning: Voltages here can easily kill. Wear some rubber gloves, and be very slow, cautious. Also, be careful not to crank the voltage too high to make brightness increases. It could cause damages. Both dials are probably hot-glued in place.. but its easy to break the seal to make them turn. Once you set them to your liking.. dab some hot glue on the new position to keep them locked in place)
If you adjust the Focus a little off, it will help smooth out the jaggie effect, making edges more soft and rounded...as well as slightly increasing the bleed effect.
The individual color guns can also be de-calibrated a bit (convergence), so that they are not perfectly aligned. This can also help in smoothing the image a bit. This is another thing that used to happen quite naturally in the arcades. Games got man-handled a lot.. and moved around in the arcade as well... so the dials would often shift.. and or the gun alignments would get decalibrated from the mere physical world aspects.
The other thing that happens to arcade crts, is dust build up between the monitor glass and the bezel glass. It should happen naturally on its own. It creates an additional fuzzy warm glow.
I believe colors are also quite different between monitor ages. Partially due to the larger CRT mask holes + light leak. Additionally, the circuitry may also have played a factor as well. I know that many TV CRTs have the abilities to adjust the color-space. By doing this, you can get different looks that are not possible using just the standard brightness, contrast, tint, and color sliders. The elder CRTs may have this only accessible in a secret option menu that repair techs use. And even older models.. might only have internal pot dials to adjust.. if any adjustments are possible at all.
There are sometimes color tweak dials on the main mini-board that connects directly to the tube. That might help, but its doubtful it will alter the colorspace values.