You can say that there is a near miss when something is nearly hit by another thing, for example by a vehicle or a bomb. Details have been given of a near miss between two airliners over southern England earlier this week We've had a few near misses in the raids, as I expect you've noticed. = narrow escape
A near miss is an attempt to do something which fails by a very small amount. Milan's successful defence of the European Cup and near-miss in the Italian championship last season