Nothing makes a fish fillet look as tempting as those deep brown, seared-in grill marks. You can get them on your fillets, even when the weather's not good for grilling, by using a grill pan. A cast iron grill pan in particular is handy; just season it well. Seasoned cast iron cookware helps prevent the fish from sticking to the grill pan and falling apart when you try to flip it or take it off. Cooking fish fillets in a grill pan takes only a few minutes, and it requires less fat -- and makes a lower-calorie dish -- than pan searing.
Defrost frozen fish fillets before cooking them on a grill pan; otherwise, the outer layers of meat overcook before the center is safely cooked through. Most fillets defrost in 12 hours or so in the refrigerator. If they're sealed in airtight packaging, thaw them by submerging them in cold water for 45 to 60 minutes. Replace the water after a half-hour with new, colder water.
Remove the fillets from their packaging and blot them dry with paper towels. Brush both sides of the fish with cooking oil or melted unsalted butter. Season them to taste with salt, pepper and any other herbs, spices or aromatics you want to use. Citrus zest, minced garlic, dill, rosemary, tarragon, thyme, curry powder, pre-made seafood rubs and blackening or Cajun seasoning mixes are a few options that complement stove-top fish fillets.
Heat the grill pan over medium-high heat for several minutes, until it's too hot to hold your hand right over it. Lay the filets on the grill pan, skin-side up if they have skin. Leave them in place for 1 minute so the grill pan marks sear in nicely. If they don't easily release from the pan when you slide a broad spatula underneath them, sear for a few more seconds until you can remove them easily. Rotate the fillets 90 degrees and cook for another minute to create a crosshatch pattern.
Turn the fillets over carefully with the spatula. Take care to support the whole fillet to prevent it from breaking apart, as most fish starts becoming flaky as it gets close to done. Cook the fillets on the second side until the flesh becomes completely opaque all the way through to the center. Thinner fillets may only need about 1 minute after turning, while thicker cuts may need up to 7 or 8 minutes after flipping.