I stopped having caffeinated coffee to prove to the OH it would make no difference to me. I used to get a lot of headaches and well as being fairly tense and tetchy.
I did it for a month, got through the withdrawl (including even worse headaches!) to find that I rarely got the headaches and I was so much more relaxed. This was at the end of last summer. I still now drink decaf coffee. I don’t worry so much about tea as I don’t drink nearly as much tea as coffee. So I did have to admit that he was right… it did help! 
If I do get a headache now it is usually if I’m dehydrated or hungry.