Combine parsley, rosemary, oil, lemon zest, and a pinch of salt and pepper in a large bowl, stirring to combine. Add swordfish cubes, tossing to coat. Cover tightly and refrigerate at least 3 hours and up to 6 hours.
Thread swordfish cubes onto skewers.
Preheat a large grill pan to medium-high. Brush pan with oil.
Place skewers on pan and sear 3 to 4 minutes, then flip and cook 3 to 4 minutes more, until swordfish is opaque and just cooked through.
Sprinkle lemon juice over fish just before serving.