Decorously means in a decorous way: you sit, speak, wait, or dress so that you look right for a serious or formal moment. She waited decorously means she waited quietly, without making a fuss. You meet it in writing more than in speech, often in older stories or careful descriptions of manners. Though actually, it can sound stiff, even a little funny, if you use it for small everyday things. Nobody needs to eat a snack decorously except as a joke. Save it for ceremonies, formal rooms, and moments when someone is trying not to break the mood. It is not a warmer word than politely; it is narrower. Politely can be kind in the shop. Decorously is politely with a straight back.