At someone else's house, I still use a corner or just face them to the wall.
At the supermarket, I reafirm, to "stop that " and sometimes, I just pick her up and hold her tight, and then talk quietly about why that behaviour is not good. I usually offer a reward if she remains a "good girl" ( like an ice cream after shopping) The main thing I find if out and about in public is not worrying what others are thinking of you and the noise. It is sooo much more important to deal with your child in your way, than whether the lady next to you is glaring at you because of the tears and noise.