It is a big mitzvah to comfort the bereaved, for example by visiting mourners at the shivah house. It is normal to feel awkward around death and not to know what to say. The Jewish laws of mourning are carefully crafted to allow mourning and ultimately healing to happen, but sometimes they can be followed in a way that has the opposite effect.
One example is the halachah that one should not greet mourners but rather wait for them to initiate the conversation. The idea is not to bombard the mourners with small talk and pleasantries. Cheery hellos can sound meaningless and even offensive to a grieving heart.
Instead we wait for the mourner to speak and say whatever they feel like saying. There is great wisdom in this, but dogmatically applied, it can cause discomfort and stilted conversation. Probably the most comforting things at a shivah are to show up, be real and express genuine empathy.