Preheat grill to medium-high heat.
Using kitchen shears, cut along the top of the lobster shell to expose the meat. Gently pull the shell apart, leaving the meat attached at the tail end. Remove the vein running through the meat, if desired.
In a small bowl, whisk together the olive oil, lemon juice, minced garlic, dried oregano, dried basil, salt, and black pepper.
Brush the marinade over the lobster tails, making sure to coat the meat well.
Place the lobster tails on the grill, meat side down, and cook for 6-8 minutes. Flip the lobster tails and cook for an additional 6-8 minutes, or until the meat is opaque and cooked through.
Remove the lobster tails from the grill and let them rest for a few minutes before serving.
Garnish with fresh parsley and serve with lemon wedges, if desired.