This is probably pretty obvious for the sisters, but maybe not for the brothers. A few years ago I was in a situation where I needed a Priesthood blessing. I did what I thought I only needed to do: I called my home teachers. Unfortunately at that time my home teachers consisted of a High Priest and a Deacon, which meant only one could give the blessing, and that one person was unavailable.
To make a long story short, phone calls were made and one brother from my Ward was able to come to provide a blessing. Afterwards the people who knew of my situation forgot about what was going on, so no further assistance was given. In other words, I fell through the cracks.
In order to prevent this from happening again, I sat down with my home teachers and Bishop and we came up with a plan for me to have a list of backup names and phone numbers. Along with this was the instruction that the Home Teachers would also have the names and phone numbers of my Visiting Teachers so that calls would be made and more people would be aware of the situation. I would strongly urge other widows to do the same.
Priesthood Backup List
Immediate family members (if applicable)
High Priest Group Leadership
Elder's Quorum Presidency
Having something like this already in place can provide some order, as well as peace of mind, during emergencies when it matters most.