Toast chiles in a dry frying pan over medium heat until fragrant. Put in a small bowl, cover with warm water, and soak 10 minutes. Drain and coarsely chop.
While chiles soak, heat a grill to medium (350° to 400°). Tear two or four pieces of aluminum foil, each slightly larger than the fillet that will sit on it. Using a toothpick, poke holes 2 in. apart on foil. Rub fish all over with oil, season with salt and pepper, and set on foil sheets.
Beat butter with a mixer until pale and fluffy. Add chiles, garlic, and cilantro.
Grill fish on foil (close lid on gas grill) until firm and bouncy when poked, 8 to 10 minutes. (Or, cut to check; fish should be just opaque throughout.)
Transfer fish to a platter. Immediately spoon about 1 tbsp. chile butter onto each small fillet or 2 tbsp. onto large ones. Season with a squeeze of lemon juice.
*Both of these chiles are mild and fruity, but anchos are slightly hotter. If you're using guajillos and want your sauce to be a bit spicier, leave the seeds in one of the chiles.