It may be hard to believe, but rats can not actually vomit. They also cannot burp and they do not experience any heartburn. The reason for this is because of several reasons. Rats have a strong and powerful barrier that is situated between the stomach and the oesophagus. Rats do not have the oesophageal muscle strength to be able to open the barrier by force, which is what is needed to actually vomit.
Another reason why rats cannot vomit is because of the actions of their diaphragm. When vomiting, it requires the two muscles of the diaphragm to be able to contract independently, and in rats there is no evidence of them being able to do this.
Rats also do not have complex neural connections in the brain stem to be able to coordinate the muscles needed to be able to vomit. So you will never see a rat vomit. If they do eat something which upsets their tummy they simply do not eat it again.