Good morning Karen, I'm sorry for your loss and I'll try and help you as best as I can.
Firstly which email account is it? (Gmail / Yahoo/ Hotmail etc) You will find that each provider has different steps in place to facilitate account recovery in your situation.
Below are the respective solutions for each type of email account.
Microsoft / hotmailhere - need to fill in a form or here.
I also found this article with the following info:
Login from that user's computer
Many users save their passwords and usernames on their computer. Sometimes logging into their accounts from their computers allow you to access the account and modify or delete it. Unfortunately, if you do not have the username and password for the computer, this may not be possible.
Non-transferable or accessible accounts
Some companies have strict policies when it comes to accessing or deleting a deceased account. These policies may prevent an account from being deleted, even if requested by a family member of the deceased. Many times, the only method of getting the account removed or accessible is by court order.
Let expire
In the case of e-mail accounts, letting the e-mail expire is often be enough for most people. Over time, an e-mail account fills up or expires (often within a year). However, this may not always be the case for every company. Before resorting to this last suggestion, make sure the company will remove the account if inactive.
Regards Karen