One of the supposed benefits of monetary union is that it leads to an increase in trade. The basic mechanism is that the exchange risk disappears and thus also the (implicit) insurance cost of that risk. How large the impact of this particular trading cost is, or its disappearance, is not well established in the empirical trade literature.
Douglas Campbell tacks a new tack at this question using a dynamic gravity model. He uses historical instances of countries breaking away from a currency union, thus the question is somewhat different from what I indicated in the leading paragraph, especially as the dynamics may be quite different. Also, the circumstances leading to a breaking up (think of the current possibility of Greece leaving the Euro) can lead by themselves to fluctuations in trade, especially in the short term. It appears, the earlier literature largely ignored these circumstances. Taking them into account reduces the impact to a measly 1% of trade volume, although quite imprecisely estimated. The consequences of Greece leaving the Euro may thus not be of much significance, especially on the trade front.