Each display device renders colors in their own way. E.g. Apple's retina display renders colors in a more vivid way then an LG display device. The photo editor has to deal with this problem. I use my own taste when performing color correction or improving (selective) color saturation. Sadly, when a color suits my taste on my screen, it doesn't on another screen.
How can I find the ideal color saturation balance taking multiple display devices in mind?
As you say, each display renders the images differently.
The most you can do is use a device to calibrate your monitors. There are several makers and models on the market right now, some of them cheaper some of them very expensive and offering features that one would need only for professional post processing.
What is this monitor calibration doing?
A device mounted on your screen, together with a software is displaying a set of colours and measuring the actual output, then is adjusting brightness, contrast, saturation, colour hue, white balance and so on, till it reaches some kind of "common ground" that would display very similarly the image as it would have been displayed on another calibrated monitor.
The more professional/expensive devices also read the ambient light intensity and colour to achieve an even better calibration of the monitor. The way an image looks on your monitor also depends on the available light in that room and the way this light is hitting your screen (there should be no light directly hitting your screen).
My favourite photography education website, Cambridge In Colour gives a more detailed explanation of what I said above.
If you are interested in buying such a hardware tool, you can search on amazon for "monitor calibration photography"
In case you want to print what you are processing on a calibrated monitor, you should also consider calibrating your printer. Though this process is a bit more complex and expensive. If you don't have to print too often, you might rather use the services of a professional printing company.
calibrating printer I am referring to measuring the output of the printer with a colorimeter or spectrophotometer, depending on the needs and available budget and then creating an ICC profile for the printer/ink/paper combination.
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printer calibration. There are already questions and answers on this subject.
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