In a small bowl, combine the butter, zest, herbs and garlic. Mix until everything is well mixed. Season, to taste, with salt. If using right away, keep the butter at room temperature. If making ahead, reserve in the refrigerator and bring to room temperature before using.
Remove the salmon from the refrigerator and let come to room temperature. Season with salt and coat with olive oil. Brush and oil the grill. Place the salmon, skin side down, on the clean, preheated grill. After 2 to 3 minutes, rotate the salmon 90 degrees to create cross-hatch grill marks on the salmon skin. Cook the salmon for another 3 to 4 minutes. As the salmon cooks it will turn from translucent orange to opaque pink.
Turn the salmon over and cook for another 2 to 3 minutes. If the salmon starts to burn, or the flames flare up move the fish to a cooler part of the grill.* Remove from the grill and top with the room temperature compound butter. The butter should act as a sauce and melt over and coat the grilled salmon.
*Tip: It is a general rule to cook fish for 8 minutes per inch of thickness. I like salmon cooked to about medium, so I cook mine for a little less.