What type of beer is it going to be? Mugwort is potent, so don't overdo it, especially if you're using hops as well. If I were to use the two, I would probably use mugwort as the bittering agent (20 min boil should do) and just use aroma hops at the end of the boil. Or, if you wanted a mugwort aroma, you could reverse that and boil the hops for an hour and the mugwort for the last 10 or so minutes.
If you're doing the former, I would say 1oz max. If you're going for mugwort aroma, then 1/2oz should do it for the short boil, without making it too potent. Once again, it depends on the character of the beer you want.
Also, mugwort is antiseptic, like hops