Wash and rinse pint canning jars and keep hot. Prepare lids according to the manufacturer's directions.
Wash and peel carrots well. Wash again after peeling and cut into rounds about 1/2 inch thick.
Combine vinegar, water, sugar, and canning salt. Bring to a boil and boil gently for 3 minutes. Add carrots, return to a boil, then simmer until half-cooked, about 10 minutes.
Place 2 teaspoons mustard seed and 1 teaspoon celery seed in each hot pint jar.
Fill jars with hot carrots, initially leaving 1 inch headspace. Cover with hot pickling liquid, adjusting final headspace to 1/2 inch. Remove air bubbles and apply lids.
Process pints in a boiling-water canner for 15 minutes at 0–1,000 ft, 20 minutes at 1,001–6,000 ft, or 25 minutes above 6,000 ft.
Cool undisturbed for 12–24 hours and check seals. For best flavor, allow jars to stand 3–5 days before eating.