Pat the ostrich fillets dry with a paper towel. Season with salt, black pepper, garlic powder, and rosemary.
Heat olive oil in a pan over medium-high heat until hot.
Cook the fillets for 3-4 minutes per side for medium-rare, or 4-5 minutes for medium.
Optional: Add butter in the last minute of cooking and baste the fillets for extra richness.
Let the fillets rest for 5 minutes before slicing.
Serve with grilled vegetables, mashed potatoes, or a fresh salad.