Have you tried to withhold food for a few hours after vomiting so she has a chance to get that belly calm down?
I saw another member here recommend feeding meat babyfood after 4- to 6 hours of no food to see if that stays down-or try cooked chicken. My cats wont touch cooked chicken unless its rotisserie type.
Have you been to the vets for a checkup? This is just general questions-most people recommend a vet visit in the beginning of answering questions.
Are there dental problems?
What about bloodwork values?
Sometimes vomiting is food allergy, sometimes they eat too fast. sometimes its their kidney/liver values too high. The best thing to do is blood work this week to see whats going on.
At 13 its possible it could be an underlying issue-but bloodwork is the starting point about solving issues.
also is it indoor or outdoor> sometimes parasites can cause vomiting-what about the poop? Is it consistant?
Constipated kitties can throw up as well.
Hard to say without more information about health history/stress factors in the house-other pets/children-people who have recently moved in or moved out.
Or change in routine.
For now I would withhold food for 4 to 6 hours and reintroduce slowly-raising dishes higher so they don't have to hang head over to eat.
Then tomorrow call the vet for a checkup if it returns.
I second the question about a vet checkup. Just going by her age, throwing up can indicate so many things, or it can be nothing at all. In hindsight, I think it was my Lucky throwing up in my bedroom every day for about a month before he got sick. I've never been 100% sure, but that was my suspicion.
What is the vomit like? Does it look like they digested the food at all? Or does it look like they just threw up what they just ate, before it got digested? Or does it just look like foam?