I work for a very large multi-national corporation. We have an office romance policy - relationships are fine, but the two individuals can't work in the same department.
I'm employed as an individual technical contributor in the engineering department. The manager of the safety department has begun to show a lot of interest in me.

Our workplace is big on mentoring and there aren't many women in technical roles, so I didn't think much of it when this manager invited me to attend networking events after hours. Other times groups of us would get together to watch sporting events - the big rivalry games especially.

In the last few weeks this manager has been focusing more attention on me specifically. There have been a few invitations to after hours events (mostly watching the Yankees games at local watering holes). I assumed that the invite was extended to others, but that seems unlikely since it turned out to be just the two of us out.
He began to share a bit about his personal life - the marriage that fell apart, the children that are nearly grown, how lonely he he is.
This is a great guy, and many of my friends are men, some are even male coworkers, but this seems like a mine field to me.

During the last game get together the manager was a bit too affectionate - touching my arm, rubbing my shoulders, complementing my hair and nail polish. Then he leaned in and kissed me.
He immediately looked bashful and told me "I really like you. You know, I think you hang the moon." I assume looked a bit like a slack jawed fool - that's how I felt. Perhaps I was naïve, but there's a 20 year age difference between us, so it never crossed my mind that anything beyond a professional and possibly friendly relationship would ever be on his mind.

This isn't in violation of company policy, and all his flirting is taking place outside of work hours, and this manager is not in a position to promote or demote/fire me, but he is in a position of power in my company, and our departments work together on a fairly regular basis. I feel like I'm just along for the ride at this point. I didn't catch on early enough to put a stop to it while I still had some power.

What is my best step from here?

I always thing ( what I call fishing in the company pond) is a bad idea, if the break up latter goes real bad, it is hard to keep professional all the time at work.
If things go real good, it can also inhibit your professional growth since it is now two carreers not just one in that company, you may get offers to move to other locations for promotions and he would not, or so on.

And you always have the "power" it is the word NO

Be "busy" and don't attend these "after hours events." He's a coworker in the same company and is married with kids, so hands off.

(You're a good writer, by the way.)

Act like your starting a relationship with someone outside of work. Tell co-workers how great this pretend guy is, etc. If your manager questions you about this quick relationship, tell him that you are sure he wishes you the very best. If he gets nasty go to HR.

Be "busy" and don't attend these "after hours events." He's a coworker in the same company and is married with kids, so hands off.

(You're a good writer, by the way.)

I was under the impression that it was a marriage that fell through, hence divorce. Am I right? If not then back off.

On the chance that I did read correctly and assume the correct situation was in affect. I would still say back off. (that was a lot to write just to say back off).

I only say that because I agree completely with the first responder.

I tried to edit/update my Question, but I keep getting an error, so I'll comment this way instead.

I completely agree with everyone who is saying to back off and get out. - I have no desire to be involved with anyone from work, especially not someone in a senior position. However, even if we did not work together I wouldn't pursue a relationship with this man; I don't have any personal interest in him. This man is my mother's age.

I guess I wasn't 100% clear, my request was intended to seek advice about how to proceed with removing myself from this situation delicately.
I don't want to hurt my career. I see no need to cause waves and damage his either though - assuming he let's things go and doesn't attempt a repeat performance. I do still need to work with him and his direct reports, so ignoring him or being rude isn't much of an option.

I'm fairly timid and he's a boisterous Italian New Yorker, so "Just tell him to back off" isn't very useful advice!

Thanks everyone!

(And yes, you're correct ITStudent, he hasn't been married in over 10 years now.)

Have you tried acting like you are already involved with someone else. He doesn't need to know that you really not. Let everyone you work with know that your involved with some great guy and NOT available any longer period. If your supervisor question you, just say fell in love first site. Just keep going on about how happy you are, blah,blah. Go as far as to send yourself flowers at work, with this pretend guys name. The only reason I would suggest this route versus confronting your supervisor directly is because you obviously feel your job will be in jeopardy.

I think the ship has sailed on any tricky ways of getting out this like lying about another boyfriend or a new relationship. I have to counsel that gently honesty is your best approach here. Emphasis on the honesty part.

Sometimes it is hard to let your mouth say the awful true things, but you have to try. Practice ahead of time, write it down to get the phrasing just like you want.

Things you'll need to be able to include are:

1) I'm so sorry I didn't notice your attentions earlier
2) I enjoy your friendship but aren't interested in anyone as different in ages as we are, even someone I already like as friend, like you.
3) I blame myself for not realizing I should have made this clear earlier, please forgive my naïveté.
4) I'm just sick at the thought that I have to hurt you this way, I value our friendship so much.
5) Can you forgive me for not being interested in you that way?

It's hard, it's doable, it's a must. This has to be honest.