The fundamental problem may end up being the tube used by the monitor. If they aren't the same, then the phosphors may be slightly different and different enough to make matching impossible.
The other thing I can think of is to try:
Make sure that on the monitor settings you set the colour temperature to the same value if possible. This may end up being a "look at it and see" exercise.
By the way, this colour matching thing is why Pantone colours are so important in electronic publishing. Designers will use their printed swatch of Pantone colours to choose the one they want and use Pantone 465 or whatever in their graphics program so that when it prints out it will look consistent (note consistent rather than the same).