A company owned by Australia's richest woman will have to pay the costs of a journalist who the billionaire tried to force into revealing her sources for a book about the family.

The Supreme Court of Western Australia on Friday dismissed Hancock Prospecting attempt to not pay the costs awarded against the company in a long-running battle with Fairfax Media's award-winning journalist Adele Ferguson.

Mrs Rinehart's Hancock Prospecting took action against Ms Ferguson and Fairfax Media in 2013 demanding she hand over emails, text messages, notebooks and any other material she had regarding conversations with Mrs Rinehart's son, John Hancock.

It was claimed the material was needed for a private arbitration hearing between Mrs Rinehart and her son in Sydney.