Carotid endarterectomy is mainly for people whose carotid arteries are blocked 50 percent or more. For the procedure, a surgeon will make a cut in your neck to reach the narrowed or blocked carotid artery. Next, he or she will make a cut in the blocked part of the artery and remove the artery’s inner lining that is blocking the blood flow. Finally, your surgeon will close the artery with stitches and stop any bleeding. He or she will then close the cut in your neck.