How does limitation of liability work for shipowners?

It can be. Under the Maritime Transport Act 1994, which incorporates the international Convention on Limitation of Liability for Maritime Claims, shipowners and certain others can limit their liability for many types of maritime claims to an amount calculated by reference to the ship's tonnage. Claims for property damage and personal injury fall into different categories with different limits. The right to limit is not available if the loss resulted from the person's personal act or omission committed with intent to cause such loss, or recklessly and with knowledge that such loss would probably result. Limitation does not prevent you from proving your loss, but it caps the amount recoverable. Get legal advice about challenging the right to limit and check whether the ship's insurer, often a protection and indemnity club, is involved.