Guardedly is how you do something when you are being guarded. You speak guardedly: you choose your words and you do not say the whole of what you feel. A minister might answer guardedly when a reporter asks a hard question. You can smile guardedly, agree guardedly, or talk guardedly about the future — yes, but not with an open heart. It is the same idea as guarded, used of the action, not of the person. Though actually, it often sounds a little formal, the kind of word you meet in news and in careful talk, more than in a chat with friends.