Antiques carry two kinds of risk regular furniture does not: fragile original finishes that modern tape and plastic can strip, and a monetary value that a repair or refinish would only lower, not restore. Document, handle with clean hands, and consider a specialty mover for anything truly rare.
Pro tip: Get a professional appraisal before a long-distance move if you do not already have one; it establishes value for insurance purposes and for your own records.
Watch out: Tape applied directly to an antique's original finish, paint, or gilding can pull it off when removed, permanently reducing the piece's value.