But 71 percent voted "no" to the proposals, according to official results published by the Swiss news agency ATS.
Rejection of the initiative was "a strong sign for the public service and for private regional radio and television," said the Swiss Broadcasting Corporation (SSR) director Gilles Marchand.
He said note had been taken of criticism of SSR and announced an efficiency drive and 100 million franc ($106 million) investment from next year.
No Billag's backers, led by the youth wing of the libertarian Free Democratic Party (PLR), sought to portray the SSR as an unfairly dominant and outdated relic.
Switzerland's largest party, the nationalist and anti-migrant Swiss Peoples Party (UDC), had also thrown its support behind the initiative.
SSR, which received about 1.2 billion Swiss francs from the licence fee last year -- or three quarters of its budget -- delivers news in the country's four official languages: German, French, Italian and Romansch.
Many credit it for guaranteeing that all Swiss residents receive information of crucial public interest in all four languages, along with a range of opinion and analysis.
But No Billag's proponents argued that freeing taxpayers of the 451 Swiss francs annual fee would unlock new economic potential, create a more competitive media sector and ultimately foster more choice.
The cost is due to drop to 365 francs next year, but everyone will have to pay, even if they do not own a television or radio after the government decided both platforms were watched and listened to via the internet.
Sunday's poll was part of Switzerland's direct democracy system, where proposed initiatives face a national vote four times a year.
Turnout reached 54 percent, nearly 10 percent above the recent average for such votes in Switzerland.
The campaigns are often muted in politically tepid Switzerland, but sometimes -- as with No Billag -- temperatures rise.
A broad political coalition along with prominent athletes, filmmakers and even the chief executive of top Swiss bank UBS, Sergio Ermotti, came out in defence of public media.
The committee formed to fight No Billag underscored the dangers of a fully profit-driven media environment in multilingual Switzerland.
It warned that with a substantial majority of the country's wealth concentrated in German-speaking areas, programming would increasingly skew to that audience.