Vomiting can be a sign on gastrointestinal parasite infestation, most likely from protozoa. I know only one of your frogs is throwing up, but both frogs need to be treated since they share the same enclosure. If a fecal sample can be produced from either frog before a trip the vet, it would help a lot in diagnosis. To test properly, the sample should be no more than 24 hours old and it can not be harvested from the frogs' water bowl.
Since neither your location or country are displayed in your profile, I find it hard to reccomend a vet for you. Thats why we ask our members to post them. Its helps us a lot to help you.