Thai authorities have convicted two bar workers for the murders of the British backpackers, amid allegations that the suspects made confessions under duress.
Mr Miller and Miss Witheridge were brutally murdered on the holiday island of Koh Tao in September.
Zaw Lin and Wai Phyo have been sentenced to death.
Dozens of people have marched in protest in Myanmar, also known as Burma, to call for the release of two men sentenced to death in Thailand for murdering two British tourists.
Around 200 protesters led by Buddhist monks marched to the Thai embassy in Yangon, holding banners reading 'Free Zaw Lin and Win Zaw Tun'. Some chanted "We want justice" urging Thailand to reconsider the murder case.
The verdict followed a trial that saw prosecutors build much of their case around DNA evidence that police said linked the two migrant workers to the crime.
Defence lawyers argued that police had mishandled the DNA evidence and that the two men were tortured while in detention. The lawyer for both men said they will appeal within one month.
Protesters in Yangon appealed to the Thai authorities to reconsider the verdict.
Watch footage of the protest here:
The group has vowed to return for another demonstration on January 2, 2016.
David Miller from Jersey, and Hannah Witheridge from Norfolk were found dead on a beach in Thailand in September 2014.
The Miller have told ITV News they are against the death penalty issued to the two men convicted of David's murder. The pair are appealing.
A human rights activist defending the men found guilty of murdering David Miller says the 'botched' investigation can't prove their guilt.