Although the play is titled "Antigone," the protagonist is arguably Creon. He is the one who is destroyed as a result of his actions arising from his tragic flaw (rather like his brother-in-law Oedipus). The climax would then come at his discovery of the result of his actions: the finding of the bodies of his neice and son. At this point Creon has lost the things most important to him, and he realizes the consequences of his hubris.

In literary terms, a climax occurs when the reader knows who "wins" a conflict. In my opinion, the climax occurs in Scene VII, in which Antigone is discovered to have hanged herself. It is a grim win, but a win nonetheless. Creon is not the one who will decide her fate.

Antigone's suicide is one a series of tragedies, all resulting in Creon having lost his battles. His son Haemon has also died (by an accident of his own hand). Here is a summary of that scene:

A messenger enters and reports that Haemon has taken his own life. Eurydice, Creon's wife, comes from the palace to receive this information. She learns how Creon and his men first gave Polyneices an honorable burial, and how, when they came to Antigone's crypt, they found that she had hanged herself. Haemon, in grief, tried to stab his father and, failing this, impaled himself. Eurydice bears this news in silence, returning to the palace.

The conclusion of the play will bring all the tragedy home to Creon, who will eventually lose everything, including his wife. Eurydice, too, takes her own life.

What is the climax of Sophocles' play Antigone?

The climax is always the most emotional moment of the story, but also the moment that points towards the resolution. While the resolution does not yet take place, the audience/reader can definitely see an unwinding in the story line begin to take shape.

While the moment that Antigone is led to the tomb is certainly very emotional, the action of the play continues from that point, so the climax occurs further into the play. The climax actually occurs after Tiresias has relayed his prophecy of doom and Creon has finally relented and asked the chorus for advice on what to do. After they advise him to release Antigone, he finally yields and says:

Alas, it is hard, but I give up what my heart wished to do
...
I bound her and I will go and release her,
for I fear that it is best to keep
the established laws as long as one lives. (1114-15, 1120-23).

When Creon says "the established laws" he is referring to the laws of the gods and finally yielding to Antigone's belief that he should not have passed a decree that attempted to overthrow the gods' authority. However, we soon learn that Creon has changed his mind too late. Soon after this, we learn that Haemon, Antigone, and Creon's wife have all committed suicide, leading us to Creon's devastation and the tragic resolution of the play.

Therefore, the climax of the play is the moment when Creon finally relents and changes his mind, but all too late.