It depends ...

When requesting a calibration it is reasonable to try and establish beforehand something about the measurement uncertainties that are likely to be provided on the ensuing certificate; unless they are going to be adequate there is not much point in asking for the calibration. But purchasers of calibration services should be wary of promises, made in advance, to provide a specified uncertainty because it cannot be determined until after a device has been calibrated. It might, for example turn out to work well, not very well or have a pressure-independent output (translation: be broken). It is always worth checking that the uncertainty being claimed is a properly calculated uncertainty in the measurement - which attempts to take into account all the factors that might influence the device when it is in service - and not simply the potentially misleading uncertainty attributable to the measurement standard being used to perform the calibration. The latter figure is bound to be lower (higher accuracy) than will be achievable by your instrument.

When trying to provide the lowest levels of uncertainty (highest accuracy) the final uncertainty in the measurement will depend to a greater degree on both the performance of the standard on the day it was used (and at the sharp end performance is never constant) and the way your instrument performed during the calibration. So, calculation of the uncertainty in the measurement, which is based on statistical processing of real data, cannot be undertaken until a calibration is completed.

This is not to say that a good approximation of the likely result cannot be given in advance, provided that the estimate is accompanied with an assortment of 'assuming it behaves well' caveats. But if a calibration laboratory guarantees a state-of-the-art uncertainty in the measurement before undertaking a calibration you are being misled and it might pay to find out why they are making an impossible claim.

You will probably find that successive results from calibrations of an instrument, even against the same measurement standard, vary a little. This may reflect changes in its metrological characteristics but not necessarily. Small differences in results are invariably observed; even if the instrument being calibrated were to perform identically (which is ultimately impossible - it would be breaking the laws of physics) the tiniest variations in the calibration environment or procedure will produce slightly different results. The statistics used to calculate measurement uncertainties are aimed to take this into account but are not perfect in themselves - they have their own uncertainties. As a rule of thumb, little significance should be given to a measurement uncertainty varying by about ±50%. This point is generally not appreciated, though, and more information can be found in the answer to the FAQ: 'Is a measurement uncertainty of, say, 0.095% meaningfully better than 0.10%?'