First we have to decide if we address the person formal or informally in order to choose the verb form.
Here, "Perdóneme" is formal (like in: "Forgive me, sir/madam) and "conocerte" (meet you) informal (btw, I think it should be "reconocerte" (recognize you)
Thanks a lot for your corrections. In this sentence the person is adressed informally, and yes, it should be "recognize", so if we say "¡Perdóname! No he podido reconocerte." will it be correct now?