Exhibit confidence. Know who you are, and don't lose sight of it. An older, mature man has been through many of life's ups and downs. He knows who he is and what kind of partner he wants. So should you. Take care of yourself. Though external features are important to all men, older men tend to focus just as much, if not more, on internal features. Accept those traits about yourself that fall short of perfection. Love yourself, making it easier for him to catch on.
Cultivate your own life. Give him his space. He had a life before you met him. With luck, you had one as well. If you didn't, do not make the mistake of making him your life. Get your own and quickly. Older men don't tend to go out to a club every weekend like younger guys. An older man probably won't have all of his friends over to play the latest video game, but he enjoys doing something and going somewhere. It's best if you don't try to cut in on or change that. Let him have his moments, and while he does, have yours. He'll appreciate you more for maintaining your own fulfilling life rather than trying to spend all your time attached to him.
Compliment him. Talk him up. Make him feel good and appreciated. Thank him for the little niceties. This lets him know you pay strict attention to him and his ways. He doesn't have to worry that you may try to take advantage of him. You can let him know that you don't take him or his actions lightly by acknowledging his thoughtfulness and care. Recognizing and being grateful for certain behaviors usually encourages more of the same, but be genuine in your praise. Sincerity goes a long way. Let your kudos be real and not just for flattery's sake.
Avert game playing. An older man has seen it all when it comes to dating and relationships. He's not only seen the game, he's played it and probably has been played by it. Be straightforward in your communication with him from the beginning. There will always be men who play games for selfish reasons, but most older men have a tendency to be very candid. Whether seeing someone else, not quite ready for a relationship, or is serious about dating only you, an older, confident man usually is pretty plain and open. Either accept that for how it's presented or don't accept it. He'll appreciate this same frankness from you.