Shafqat Emmanuel, 38, and his wife, Shagufta Kausar, 42, were arrested in July in the Gojra area of Toba Tek Singh district following a complaint by an imam that they were sending blasphemous text messages.
Farrukh Saif, the head of Word Vision in Progress, an organisation working for the rights of minorities in Pakistan, said the couple was sentenced to death on Friday.
"They cried when told by the judge that they would be executed by hanging," said Saif.
A court official in Toba Tek Singh confirmed the conviction.
Saif, whose organization provided lawyers for the couple, said they would appeal against the ruling.
It is second such sentencing in less than two weeks.
On March 27, a court in the eastern city of Lahore handed down the death sentence to Sawan Masih, also a Christian, for blasphemy. He was arrested last year after a Muslim friend accused him of maligning the Prophet Mohammed during an argument.
Anything deemed insulting to Islam is considered blasphemy in Pakistan and is punishable with death.
The blasphemy laws were enacted in the 1980s by then military ruler General Ziaul Haq and are seen as a tool to persecute minorities.
Rights bodies have been demanding their repeal, but the government has resisted reforms for fear of the backlash from conservative Islamic society.
An estimated 1,300 people have been accused of blasphemy since 1986, according to statistics compiled by the human rights unit of the Law Ministry.