40 years old, and the same experiences. Feeling stiff the day after, some muscles aching.
Since about 2 months I have started running (building up) in a group. Not only do I notice improvements there, but also on the tennis court (condition wise during play), and very much so the day after play. Ofcourse I still feel some muscles after tennis, but a whole lot less than before.
I also stretch after playing, and not for some 5 seconds per exercise, but preferably 20-30s! That certainly helps in my case (achilles, hamstring, but!)