it depends, do you know the species as well as the variety? some are completely hardy, others hardy to a certain extent, and others only half hardy, so a lot depends on the species as to wether you need to protect them or not.

I've lost Artemisia 'Limelight' too, I reckon it's only half hardy. I have another low-growing grey leaved Artemisia (sorry I don't know the variety) and it's been fine through the last few cold winters.

If you want to keep 'Limelight' alive, I'd take some cuttings or slips and keep them indoors on a windowsill.

Yes, i agree, it depends on the type, its orientation and the geographic location.

I have an alpine aswell as a border variety and both came through unscathed - i'm in the south west so the location plays a part.
I have one type in a sheltered area and one in an exposed - so again .... location, location, location !

My 'Oriental Limelight' seems as tough as old boots - it's a thug in my garden. It survived -10 last year.

Try digging up a root and potting it up if you want to keep it safe.

Thanks everyone, I think I will half leave, half pot and see what happens!