I am a novice at late middle-aged relationships and was never particularly good at managing them as a teen or college student. I was widowed several years ago after a long marriage. Last summer I met a new neighbor with whom I quickly became good friends. We’ve gone on to do date-like things – dinner and movies, regular hikes, etc and though we both travel for work fairly frequently we stay in touch when we’re apart via email. The odd thing is there has never been a hint of romance…just a lovely friendship. I’ve gradually come around to thinking perhaps it could evolve into something more, but I don’t know how to broach the subject and am terrified that if he’s not interested in that sort of thing I could destroy what we have now. Has anyone faced a similar situation? Is there an easier way to sort these things out at 60 than there was at 16?
My advice is to do some soul searching as to what YOU want for your future.
Are you happy with friendship or do you want another long term relatrionship that centers on marriage?
Do you enjoy being independent? Like having someone to “pal around with” without worrying about making “couple” decisions? Or wishing you had someone to share more than just dinner with?
Personally, I’d be tempted to just ask, but I’m not shy. It’s been six+ months.
Is he a widower? What’s his back story?
He’s divorced…He’s on good terms with his ex who lives far away. His college-aged daughter attends school in our town and they spend a fair bit of time together. When I met him he was involved with another woman, but he broke that off early last fall. I am certainly tempted to ask, but I am shy!
I wish I lived near you, then I could ask him! 
How long had he been with the other woman? Could he still be getting over that?
I don’t know for sure, as I’ve been with the same man for 41 years altogether now but it seems to me that it’s the same as when we were young…you just know and naturally fall into holding hands, sharing a kiss, etc. if there is an attraction.
I’ve always been in the camp that if someone wants something physical, they’ll let you know. “Accidental” touching or brushing up against you, flirting, that kind of thing. Any of that going on? Or have you tried that yourself?
I’m wondering if he’d like to move forward also but he’s waiting for a sign from you.
There is some “accidental” touching and I do think there is a possibility he is waiting for a sign for me…Problem is that I’m waiting for a sign from him and we’re both relatively shy - although very comfortable in our friendship with much easy conversation.
I hadn’t considered that he could still be getting over the other woman, but that could be playing in. My sense is that it didn’t end nicely and so he could be gun shy.
If I were the then-gf I’d be wondering who this neighbor lady is he’s spending so much time with!
Is there some way to up the ante a little? Has he been to your house for dinner?
Yup…he’s been here for dinner.
Is there a way to have him over and make it a little more special? Like eating in the dining room instead of the kitchen? China instead of regular dinnerware? The good wine? Flowers on the table? Just little things that might get him to see a progression in your mind? Nothing too overt, like opening the door naked but I’m hoping he’ll pick up on a vibe.
Well… I guess I’d just ask. Something like, “Have you ever thought that we could be more than just good friends?” And then backpedal and say, “Me, neither” if he says, “Nope.” 
I am old fashioned; I would wait for him to make a move although I would help him along with some flirtation.
I wouldn’t wait. There is always the chance some other women may come along and he thinks all you want is a friendship. You should just tell him something like you said above " I’ve gradually come around to thinking perhaps it could evolve into something more, but I don’t know how to broach the subject and am terrified that if he’s not interested in that sort of thing I could destroy what we have now."
He always brings flowers when he comes to dinner, but I hadn’t thought of eating in the dining room. He doesn’t drink so I typically don’t either when he comes over or when I go to his place…This could be part of our problem…no inhibition looseners.
Movie: Sit close. Hand on knee or head on shoulder.
Hiking: Hold his hand.
If he’s interested, the next move will be his. If not, well, you’ll then know but it will be nothing so forward that it can’t be passed off as friendly affection between two people who like to hang out together.
Go have a his and her massage
Or directly say " I really enjoy our time together. You are so easy to be with."
Softer, sexier music? Did yall do anything for Valentine’s Day, even in “jest”?
That would resolve the issue, one way or another.