This is a huge subject and full of problems. The absolute worst thing is to do nothing. I've watched a few situations where the gun guy did just that and it often turns out to be a burden. Widows seem to come in 2 flavors. One that is certain her deceased hubby was worlds smartest guy. They're sure his guns are worth more than brand new. Then they feel cheated when no one wants to pay a huge premium. Even for hunting guns that end up fairly beaten up over decades of use. Guns that are still in production and available at your local Walmart. And they're sure all of his friends are vultures when they offer up the asked for appraisal. Still as bad are the fools who offer to take the guns to a local gun show and try to sell them, often for the prices she dictates. Its how you can sit for 2 full days and accomplish nothing, and then earn her hatred for not trying hard. Its a loser for everyone.
One situation I was familiar with was a widow with a very large and nice collection. A regional gun shop came in and gave her a low ball estimate. Sure not a favor, their estimate was about $200,000. She just procrastinated, and couldn't sell just yet. Eventually David Carroll got involved. She trusted him and he sold off her collection, getting maybe in the $500,000 range. Back to the early estimate. She was advised by some well meaning fool that the estimate should be the tax basis. It meant she was sitting on a $300,000 taxable gain. Not good. Worse, she was honest and claimed it, paying the huge tax bill.
If you sell the guns yourself, you do it as a "tax friendly" transaction. Meaning it was your gun, you sold it and put the money in your pocket. Often if the widow sells the guns, you will get the IRS involved. Don't do it. Its a can of worms.
I'm retired and one of my simple pleasures is to attend gun shows with my buddies. We sit and talk (all lies), and often sell a gun or two. Over a multi year period, you can sell dozens of your old guns, often getting top dollar. Or not, we don't have to sell. Buyers just can't understand us old mule like fellers, digging our heals in and not being moved by their best bargaining tactics. But if you don't pay my price, I'll just bring the gun back again. And when I eventually croak, my wife will just call David to come pick up whats left.
I view things differently from my wife. Her solution was to just let our sons, who are into guns, pick what they want (its called cherry picking) and let David take whats left. The better solution is to let David pickup what he wants on his way to a OGCA show and leave what he doesn't want. Then the kids can take or leave whats left. They already have guns to remember ole Dad. Anything else is just gravy.