Firstly, it's not much point calibrating cause the height error is actually caused by atmospheric conditions and satellite constellation, both which are variables at different times and places.
Secondly, the heights from JUPEM are based on MSL (mean sea level) whereas GPS heights are based on the WGS84 Ellipsoid.
You can calibrate a unit like the 60CSx but you're actually calibrating the internal barometer, not the actual GPS readings. I believe the unit will actually auto calibrate itself everytime it's switched on.
Yes declan is correct.
The GPS height reading only auto calibrate if you had selected that option.