In most cases, yes, grilled cheese is vegetarian as the ingredients do not contain meat. The main time a grilled cheese won’t be vegetarian is if a cheese is used which contains animal rennet (an enzyme produced in the stomach of a calves). Many cheeses do not use animal rennet so are considered vegetarian. The main cheese to watch out for is Parmesan as this always uses animal rennet. Please check the packaging of the cheese you’re using to see if it’s marked as vegetarian friendly, if you’re concerned.