Set a steamer basket in a large pot. Fill with enough water to come just below basket; bring to a boil. Add celery root and potatoes; reduce to a simmer, cover, and cook until tender, 15 to 20 minutes.
Working in batches, transfer celery root, potatoes, half-and-half, and butter to a food processor; puree until smooth. Season with salt.
To store, refrigerate, up to 1 day. Reheat in a heatproof bowl set over, not in, a pan of simmering water.