There are some very good tips in this thread. We are preparing for my mother's death as I write this, from cancer. I will not be singing at her memorial service, but doing a recitation, and possibly the eulogy. However, my kids and the other grandkids will be singing at the service, so we've already been rehearsing.

The "rules of thumb" (there are some) for getting though the emotions to deliver the sort of speaking or singing performance you want to deliver to honor your loved one aren't universal in the sense that "one always does A, B, C". However, there are definitely rules of thumb to follow that are pretty much the same as performing when you are super nervous about a performance that is really important to YOU as opposed to being nervous about a performance that isn't personal to you and your loved ones.

I agree with whomever it was who said it is just as common to falter when speaking as it is with singing in these circumstances, and the the beginning is most often the "shaky" part for most people. So I find rehearsing the song by really hitting the first few lines hard with a lot of "oomph" power gets nearly everyone through that part, and then they do fine. I learned this trick many years ago from my high school choir teacher, and it's never failed me, whether I am speaking or singing in any setting.

BTW, this doesn't mean that you necessarily sing loud or bold or anything like that. This is a mental trick of the trade, it is how you mentally "go in strong" and push yourself into performing to get through the beginning shakes. It is pretty rare, in my experience, for singers especially, to falter once the song is well underway, because then it is over before you even know it!