Benihana Inc. won’t recoup legal fees after winning a trademark dispute against Benihana Tokyo LLC under arbitration, even though a federal judge thinks it deserves to do so.

Benihana Inc. retained rights to operate in North and South America when the Japanese restaurant chain split into two companies. But, along with Asian and European locations, Benihana Tokyo continued to operate a flagship Benihana in Honolulu under a licensing agreement.

An arbitration panel ruled Benihana Tokyo repeatedly breached the branding standards...