William Lauchlan, 37, and Charles O'Neill, 51, were also found guilty of dumping the body of Alison McGarrigle, 39, at sea after the murder at Largs, Ayrshire, in June 1997. Her remains have never been found.
Yesterday trial judge Lord Pentland, came under attack at the Court of Criminal Appeal in Edinburgh for asking for a police officer's opinion on the "proof of life" report. Solicitor advocate John Carroll, for O'Neill, told Lady Paton, sitting with Lady Clark and Lord Philip, the search for Mrs McGarrigle had not been thorough enough.
The trial heard of a violent row in June 1997. Lauchlan pushed Mrs McGarrigle as she yelled: "I know what you are up to and I will make sure I see what is coming to you." She was never seen again.
The appeal judges will give their decision in writing at a later date. Lauchlan is serving a minimum of 26 years and O'Neill 30 years.