Though I am not married yet I think if my honie of 4 years now passed on I would never find anyone to replace him. But feelings change and hope lives on. As much as most of us say we would not find anyone new I think many if not most of us would. That is just life we need to go on.
Of course you have to look at your circumstances. If you have children, how old they are I think should determine if you remarry or not. I think it's wise to wait untill they are older if they are young teenagers or preteens.
I hope we never find ourselves in this situation and if you have already you have my best wishes.