What do you do with a screaming baby?

Yesterday I watched our neighbors' kids and the baby screamed for an hour and a half straight! I've delt with Ethan when he did that, it wasn't often, but when it did happen, I'd put him down in bed and leave. (Usually he was tired.) He didn't really go through the whole stranger anxiety thing that this kid has. I tried putting this little one down for a nap, like his mom said he may want, but he screamed even louder and gagged. Nothing I could do helped him. He wouldn't even calm down enough to have some milk his mom sent or even eat a cracker, he ate some of it when I gave it to him, but most of it ended up on me. Ethan was a little concerned about the little guy, so he tried giving him some toys to help soothe him. He'd say, "Here go." That didn't work, if you were wondering.
Finally, Ethan just left the kid alone, took a drink of juice and looked at him with this look. It looks to me like he is saying, "Gosh, it's really not that bad, kid!"