JEP,
In the US, it is cancel emergency, and if you want you can add that the problem (what is was) is corrected and that you are able to continue onto your destination. In fact I would encourage the pilot to add the second statement so that the controllers won't keep worrying.
Has this happened, oh yes, and it has either been a fuel starvation (forgot to switch tanks) or a carb icing problem.
Mike R
NATCA FWA