I have had many combinations of guitar and capo over the years. I use a Shubb with my current guitar, which has a low action and quite shallow frets, so the strings do not stretch much. I find the instrument mostly stays in tune, and I rarely have to retune.

The other thing that is important is good stable tuners. When you put a capo on you are increasing the string tension. If one tuner gives a little then you are out of tune. You can check this by taking the capo off; if the out-of-tune string is still out, then one tuner has let go.

I have a 12 string, and have just about given up using a capo during a performance. The octave strings are invariably out. When you look at them you can see that having a thin string right next to a thick string results in the strings being stretched by differing amounts. Physics says they must go out!