With digital calipers, clean the jaws with a cloth/paper towel, push
the jaws shut and zero them. With them still closed hold them up at a
light and see if you can see a thin gap, if you can, they either still
have a little dirt, a burr (in the sense of a ding) or are "sprung"
from over-zealously applying pressure. If a burr, stone it down, if
they are sprung you are pretty much out of luck unless you want to
lap the faces parallel (difficult) although if they were expensive
you can send them out for repair.
To determine whether they are measuring accurately you need a
standard, micrometers usually come with them but calipers don't - a
good reason to find a machinist friend and use his (or a gage block,
or known diameter dowel pin, etc)
Another thing to remember is that if you use too much force you may
be deforming the wire as you measure it - you want a light touch with