The two faced charges of defamation, which is a criminal charge in Thailand, and with offences under the Computer Crimes Act.
If found guilty they could have faced up to two years in prison for defamation and five years for breaching the Computer Crimes Act, as well as a B100,000 fine.
The charges were formally brought to trial after a complaint filed by the Royal Thai Navy. The complaint related to an article published on the Phuketwan website in July last year.
The article quoted an investigation by the Reuters news agency, which alleged that some members of the military were involved in trafficking Muslim Rohingya refugees who had fled Myanmar.
The case drew criticism from human rights and press freedom groups around the world.
Phil Robertson, Deputy Director, Asia Division, of the New York-based international rights organisation Human Rights Watch, said before the proceedings today, "This case should have never been brought to trial in the first place, and the fact that it was shows this Thai government's total lack of concern for media freedom.
"There were plenty of opportunities for the Thai Navy and its supporters to pursue an alternative course – like demanding space from Phuketwan to print opposing views and rebuttals – but instead they criminalized the matter and demanded an absolute apology from these journalists, treating them as if they were a bunch of Navy conscripts. This whole episode shows a fundamental lack of understanding among Thai government and military officials about what a free press is really about and the role it plays in democratic society.
"Thailand needs to revoke both its criminal defamation statute and the Computer Crimes Act to end this assault on media freedom. How many more journalists and NGO activists need to be marched off to court before Bangkok admits that the Computer Crimes Act has little to do with real crime and everything to do about stifling people who express views the government doesn't like?"