The seal was found buried in mud on a farmer's land near Catterick in North Yorkshire by treasure hunter Carl Richardson.
But fellow enthusiast Richard Hunter insisted he was with Mr Richardson at the time and they had previously made a "gentlemen's agreement" to share the rewards of their labours.
The oval silver seal matrix, dating from the 13th or 14th century, is now being looked after by the British Museum in London.
It shows Thomas Becket and three knights, one of which is holding a sword above his head.
Becket was made Archbishop of Canterbury in 1162 and was at odds with King Henry over the rights of the Church.
He was assassinated by followers of the king in 1170 and venerated as a saint by the Roman Catholic Church and the Anglican Church.
The seal was found in a field owned by John Wray, who had given Mr Richardson permission to use the land.
Mr Hunter, from Peterlee in County Durham, told Coroner Geoff Fell he had met Mr Richardson a few weeks before the seal was found and they had been on a few outings together.
But Mr Richardson, from Coxhoe in County Durham, who had been metal-detecting for 20 years, denied that Mr Hunter had been with him when he uncovered the seal in October 2006.
Mr Fell said the case would be referred to the valuation panel of the British Museum but told the two men that they should aim to resolve their differences.
"It's not up to me to decide ownership," he said.
"If you cannot come to an agreement, then lawyers may have to be involved and that will be costly."