S.R.
From what I can find online, most of the concern with caffeine in children is caffeine toxicity and the large amounts of extra calories from the SOURCES of the caffeine (soda, energy drinks, etc.)
One site I found (I'll put links at the bottom) said that a preschooler should be limited to approximately 45 mg of caffeine per day, or about the amount in a 12 ounce can of coke. A cup of coffee is generally perceived as having 150 - 200 mg of caffeine. I can't find much on appropriate levels for a tween, but I would probably say that one cup of coffee would be acceptable, but two might be pushing it.
As far as the tea goes, it's going to depend on the type of tea. Different varieties have different caffeine contents.
If he feels like he NEEDS these things, it's probably time to cut back significantly. If he just likes them and can go without, then maybe just cutting back a little bit to help ease your mind.
Here are the sites I found:
http://www.webmd.com/parenting/fun-and-fit-family-11/caff... (talks about caffeine toxicity)
http://kidshealth.org/parent/growth/feeding/child_caffein...
ETA: Sorry, forgot to mention, tea (and black coffee) has a lot of health benefits, as well (antioxidants and such). So, I would say do your research, talk to his ped again, and make your decision from there. Good luck!