Add the clams to the pot and let settle for a minute, then add the white wine and cilantro. Re-season with salt and pepper and cover tightly with a lid. Let cook about 5 minutes, making sure that the broth at the bottom is at a simmer during that time. After 5 minutes, the clams should have opened or be mostly open; if not, or if the mixture is dry, add another 1/4 cup or so of wine, cover and simmer until the clams are open, 1 to 2 minutes longer. Taste the broth for seasoning and add salt or pepper if necessary. Add the butter to the broth and stir to combine.
Transfer to a large serving bowl, making sure to pour the broth over the clams. (Remove any unopened clams and discard them.) Serve with crusty bread or baguette.