Varona founded a social media women's rights campaign in response to President Rodrigo Duterte's comments on women.
"After a particularly hard-hitting column, I find 50 to 80 private messages calling me a liar, an ugly woman, and mostly these are sexist attacks," she told Agence France-Presse (AFP).
"The slurs don't really bother me but the threats that say 'we know where you live, we'll see if you are as brave as you think' – that bothers me because it also happens to other journalists," she added.
RSF's Prize for Independence is awarded to reporters for resisting pressure in carrying out their work.
"Independence is very important for citizen journalism. I teach young people to be critical minded and I hope this award will inspire them," she said.
Varona, together with Indian journalist Swati Chaturvedi, were recognized for their bravery in holding governments to account in the face of persistent threats. The two were honored at the RSF annual awards, being staged in London for the first time.
Maltese journalist Matthew Caruana Galizia, who has carried on the work of his mother Daphne, murdered for exposing corruption on the Mediterranean island, was also honored at the ceremony at the Getty Images Gallery.
Established in 1985 to defend and promote press freedom, Paris-based RSF has been presenting its yearly awards since 1992.
Previous winners include the late Chinese dissident Liu Xiaobo, imprisoned Saudi blogger Raif Badawi and the Turkish newspaper Cumhuriyet.
'Journalists are under threat'
Chaturvedi won the Prize for Courage, awarded for journalism in a hostile environment.
She has faced online harassment campaigns after exposing what she calls a "troll army" operating for the governing Bharatiya Janata Party of Prime Minister Narendra Modi.
"I get a dozen death threats every day and around 15 to 20 rape threats," she told AFP.
"The whole idea of a democracy is that you are allowed to have a dissenting view. Unfortunately, the way politics has panned out across the world, journalists are really under threat. It is sad that you are called courageous just for doing your job," she added.
Some 63 journalists, 11 citizen journalists, and 4 media assistants have been killed so far in 2018, RSF said, including Washington Post contributor Jamal Khashoggi, who was murdered in the Saudi consulate in Istanbul.
A total of 55 journalists were killed in the whole of 2017.
Caruana Galizia won the Prize for Impact, awarded for work that has led to an increase in awareness of journalistic freedom.
His mother, Malta's pioneering anti-corruption blogger, was assassinated in a car bomb attack in October 2017.
'Fight for the right thing'
"It's a recognition that what we're fighting for is right," Galizia said of the award.
"It's about continuing to fight for the right thing: justice for my mother and for her stories. Everything else will follow. Hope is a word for people who have already given up," he added.
Daphne Caruana Galizia's murder remains unresolved.
Afghanistan is currently the world's deadliest country for journalists, with 14 killed this year.
RSF said 90% of violent crimes against journalists go unpunished.
The organization's secretary-general Christophe Deloire said journalists were facing a climate of distrust, fueled by politicians denigrating them.
The removal of CNN correspondent Jim Acosta's White House press credentials was "clearly dangerous for democracy," he said, adding that US President Donald Trump's way of dealing with reporters was "beneath the dignity of the office he holds."
Marking the ceremony being held in London, The Observer newspaper's Carole Cadwalladr won a special one-off L'Esprit de RSF award for a British journalist, for her work exposing data harvesting in the Trump election and Brexit campaigns.
"We've had companies and billionaires threatening us with legal action, trying to stop us publishing," she told AFP. "It is hard to publish stories. It's become increasingly difficult. There is a hostile environment for journalists now."
RSF said some 168 journalists, 150 citizen journalists and 19 media assistants are in jail. – Rappler.com