When at the funeral or visitation, don't get into one-upping the ex-wife/best friend/whoever about how much closer you were to the deceased. You may have been his sister and had a very special relationship, but don't diminish someone else's relationship and therefore their own grief over the loss. And you may be wrong about being so close!
If you want to offer help, consider offering it through a "second-ring" of bereaved attendees. At my grandfather's funeral, my grandmother just needed consolation and the presence of loved ones. As PPs have said, it is just too overwhelming to think of what they could possibly need in the weeks to come. My mom and uncle also had a lot to deal with. Having my grandmother's friends come to me and ask what they could do for her in the days to come was, IMO, a great choice. Of course I was also grieving, but nothing even close to what my grandmother was experiencing. I still had the presence of mind to remember the offers, to know who was genuine, and to call on them later with specific needs for my grandmother.