I believe relationships are harder when over the age of 40. You might think since the kids are grown and you have more free time, it would be easier. Please note that not only are you set in your ways, so is the other person. The give-and-take needs to worked on more now then ever.
Established people do not have the innocence and care-free nature we had at 20. We are not just starting life: example: how do you spend your holidays? Can you still do that, are you willing to change, are all family members willing to accept the changes? All of a sudden I was cooking for 25 people and cooking was never an interest of mine, but I was willing to change (although the cooking is still in question).
Move SLOW. Date for a long time. Don't be exclusive right away and keep time for friends and yourself. And I do not recommend dating right after a divorce or death of a loved one (or to date anyone in that catagory). I realize that I did not follow my own advise, but i can say from experience that the roller coaster ride was a huge struggle. An important point, in divorce you know that the couple couldn't overcome their issues and parted. A widow/widower still has love for that person, which will always be there and be treasured. Can you live with that?
Now, don't believe it when a person says "I was with my partner for 10 years and never cheated so I'm clean". You do not know what happened on the other side. We have enough health issues without adding a sexually transmitted one to the equation.
Old saying is "I would rather be happy and single than married and miserable".
Oh, and it is my opinion that free dating sites are questionable, but professional sites are great, also check with friends or look online for old school chums. If nothing else, you will have more friends to add to your Facebook!!!