It is said, that when a married couple separates, "the altar cries". I would like to know which altar is meant, as we do not have a temple right now.

You refer to the words of theTalmud in Gittin 90b and Sanhedrin 22a that teach that when a man divorces his first wife, the altar cries. The message obviously does not describe a physical phenomenon even when the Temple is standing in its place. What is being taught is that the connection between a man and his first wife is an expression, on a personal human level, of the connection between G-d and Israel. When that personal connection is severed, the larger connection suffers as well. The crying of the altar- connecting G-d and Israel- is a reflection of that suffering (Maharal Hidushei Aggadot Gittin 90b).