How do I make peace with my ex?

(Guys only pls). How do I make peace with my ex?

Two months ago, my ex boyfriend (33 year old) and I(35 year old) broke up after 2 years relationship. He offered to be friend and wanted to have lunch together right after we both decided on the break-up. However, I said I can't see him anymore because I still loved him very much. Now we no longer interact with each other, except for taking turns to pay cell phone bills online ( we share a family plan). But I really want to make peace with him , because I still care for him. After 2 years of living together, the break-up was like cutting a body part off.

I know very clearly that we were not made for each other and it will never change. Now I am afraid of facing the possible indifference and rejection if I initiate the communication again. Can you please give me some suggestions?