We do computer monitor calibration/profiling but is there such a thing for LCD of digital cams?

Recently, I managed to get a backup compact digital cam. I plugged in my CF card with images taken from a DSLR. The images in the compact digicam surprisingly look like they are at least 1/2 stop over-exposed. Colours appear more pale and exposure looks off. However, the histogram from both cams show the same shape... meaning the exposures should theoretically be the same, afteral, they are from the same CF card!

How do I ensure that both the DSLR and compact cam reproduce the same (or at least close to) exposure and colour? Or do I have to get used to the difference?

Thanks very much!!!