"That only works if your opponent makes a mistake. The proper way to counter an artifact spell would be to wait until
mishra's ability resolves before casting your countermagic. Since
Mishra's ability is on top of the casted spell, it would resolve first."
Fact, however there is a way around that, and it is the wackiest solution possible.
Counter your own spells.
If you run an effect that counters your own spell (
Chalice of the Void,
Nullstone Gargoyle,
Blood Funnel,
Ice Cave,
Nether Void,
Planar Chaos and
Disruptive Pitmage and the like are all in color) then they can't touch you. You cast, then counter, then the card goes into your graveyard and from there onto the battlefield.
This is from the gatherer, offical wizards website.