Panama does not have many veggie restaurants, and not all restaurants have clear vegan choices. However, Fire + Ice is actually a US-based small chain that has a branch in Panama City. It is located on Calle 49, just off the corner of Calle Uruguay. It's a pretty big space, with a Mongolian grill in the center. You can either order from the menu, or choose an all-you-can-eat buffet from the Mongolian grill. We alerted the server that we were vegetarian/vegan and the cook at the grill used a separate area of the grill, and separate utensils to cook our food (I doubt the area of the grill is only used for veggie food at all times, though). The vegetarian buffet was US$16.99 per person. Vegetarian (not vegan) items are marked on the a la carte menu.
There were lots of veggie options for the grill, including many noodles, rices, vegetables, peas, sauces. The service was very friendly, and the manager said that most of his family is vegetarian. There is meat that is served here however. The place is clean, and the food seemed fresh. Overall, given the severe lack of pure vegan/veggie options in Panama City, I'd say give this place is worth a try. Otherwise, good luck trying to figure out if your beans were cooked with lard, or if the rice was cooked with chicken stock!
Cons: Meat, No clear 'vegan' options