In the two main passages in the Bible (Leviticus 24: 10-23 and I Kings 21: 8-13) the penalty for this offense is stoning to death.
According to the Gospels of Matthew (26: 63-6) and Mark (14: 53-64) Jesus was tried by the Sanhedrin on a charge of blasphemy. In Hebrew it is known as birkat hashem, literally “blessing [euphemism for cursing] the Name [of God].” The one guilty of this offense is called a megaddef (blasphemer).
Matthew 26
New International Version (NIV)
62 Then the high priest stood up and said to Jesus, “Are you not going to answer? What is this testimony that these men are bringing against you?” 63 But Jesus remained silent.The high priest said to him, “I charge you under oath by the living God: Tell us if you are the Messiah, the Son of God.”
64 “You have said so,” Jesus replied. “But I say to all of you: From now on you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven.”
65 Then the high priest tore his clothes and said, “He has spoken blasphemy! Why do we need any more witnesses? Look, now you have heard the blasphemy. 66 What do you think?”
“He is worthy of death,” they answered.
67 Then they spit in his face and struck him with their fists. Others slapped him 68 and said, “Prophesy to us, Messiah. Who hit you?”
Mark 14:53-64
New International Version (NIV)
Jesus Before the Sanhedrin
53 They took Jesus to the high priest, and all the chief priests, the elders and the teachers of the law came together. 54 Peter followed him at a distance, right into the courtyard of the high priest. There he sat with the guards and warmed himself at the fire.55 The chief priests and the whole Sanhedrin were looking for evidence against Jesus so that they could put him to death, but they did not find any. 56 Many testified falsely against him, but their statements did not agree.
57 Then some stood up and gave this false testimony against him: 58 “We heard him say, ‘I will destroy this temple made with human hands and in three days will build another, not made with hands.’” 59 Yet even then their testimony did not agree.
60 Then the high priest stood up before them and asked Jesus, “Are you not going to answer? What is this testimony that these men are bringing against you?” 61 But Jesus remained silent and gave no answer.
Again the high priest asked him, “Are you the Messiah, the Son of the Blessed One?”
62 “I am,” said Jesus. “And you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven.”
63 The high priest tore his clothes. “Why do we need any more witnesses?” he asked. 64 “You have heard the blasphemy. What do you think?”
They all condemned him as worthy of death.