Pair these clams with some crusty bread so your dinner guests can soak up the broth.
Prepare a large bowl of ice water. Bring a large pot of water to a boil. Salt the water and add the parsley, cilantro, and tarragon. Cook until wilted, about 15 seconds. Drain and transfer the herbs to the ice water to cool. Drain and squeeze the herbs to remove any excess water. Transfer to a cutting board and coarsely chop.
In a food processor, pulse the herbs, capers, and lemon juice until finely chopped, 10 to 15 seconds. With the machine running, slowly add the oil. Season the salsa verde with salt.
In a large skillet with a lid, melt the butter over medium heat. Add the wine and bring to a simmer. Add the clams. Cover and cook, shaking the pan occasionally, until the clams open, about 5 minutes. Using tongs or a slotted spoon, transfer the clams to a bowl. (Discard any clams that do not open.) Reduce heat to low and cook the liquid in the skillet until reduced slightly, about 2 minutes; season the sauce.
Divide the clams and the sauce in the pan among 4 shallow bowls, arranging the clams open-side up. Serve the clams immediately with the salsa verde and crusty bread.