I am also sensitive to caffeine but you will be very hard-pressed to find any decaffeinated beverages in Japan. The concept is foreign to the average Japanese. When in Asia I just deal with the effects.
The amount of tea you drink in a tea ceremony is only a few sips. Even if you're sensitive to caffeine, you won't feel the effects that much.Edited: 5:45 pm, March 21, 2013
There are quite a few Japanese people who are intolerant to caffeine and many pregnant women will avoid it. However, looking at the Japanese Wikipedia page for the decaffeination process the view is that decaffeinating results in an inferior product as more than just the caffeine is stripped away.
For tea it just doesn't seem necessary as nature (and a bit of expertise) will remove much of the caffeine for you. Rather than drink green tea (Matcha, Gyokuro, Sencha, Konacha) which is high in caffeine, there are readily available alternatives; Bancha and Houjicha. Alas, the caffeine content can vary but there are numerous examples of both these teas that have less caffeine in them than decaffeinated Western teas. Other options for the caffeine intolerant are Mugicha (made from roasted barkey and VERY popular in the summer) and Sobacha (made from roasted buckwheat nibs and great for helping to reduce cholesterol levels - note that this isn't the same as sobayu/soba cooking water). In specialised stores in Kyoto and elsewhere you can find another one of my favourites, a tea made from roasted black soy beans; Kuromamecha. A delicious alternative to matcha milk (a whisked green tea milkshake that can be drunk hot or cold) is milk blended with Kinako (a roasted soy bean powder) with or without sugar.
I've seen advertisements for products aimed pregnant women who miss green tea but these include spinach and other green leaf powders and are marketed as health supplements.
I hope this post helps answer why there isn't a big demand for chemically decaffeinated tea products in Japan. As Shibuyakko has already mentioned, one doesn't need to drink very much tea in a tea ceremony. In fact, you can just take one very tiny, very brief sip, but do warn your host before hand about this.
For your own Information, the tisane that most closely resembles tea (not matcha) for me has been dried mulberry leaves. It is a product of Thailand and Vietnam.
If you want to try your hand at whisking a frothy drink with a bamboo chasen then try the Kinako I mentioned earlier. It's usually made with milk or soy milk but you can make it with hot water. With milk it tastes a little like the weak milky coffee French children dip their croissants into at Breakfast. I roast and grind soy beans to make my own kinako and stir it into warm milk as a bed time drink for my own young daughter. Makes great cookies too.Edited: 4:27 am, March 22, 2013
I investigated a little more. As suspected, there are Japanese people who know about mulberry leaf tea and want a caffeine free alternative to the powdered 'instant' green tea that is popular throughout the country:
Mulberry tea is 桑茶 (kuwacha?). It's not a particularly common drink - unlike the ubiquitous mugicha, and even sobacha is often available in vending machines - but it is around if you go looking for it.
There is no caffeine free alternative to matcha as the whole point of matcha, the way it is painstakingly cultivated and prepared, IS the caffeine - the tea ceremony was developed as a spritual and physical Proplus equivalent for meditating priests. But if mugicha, houjicha, bancha, etc don't appeal and you want a 'greener' taste then this is something worth looking out for. It'll be way more pleasant than most of the bagged green teas sold in British supermarkets.
Yotramas has done great research! Thank you! I live in Japan and never gave it much thought. Houjicha is the choice drink at dinner in many restaurants as it has no caffeine. But, you might not find all restaurants being so gracious.
I encountered my first non-caffeine Japanese tea bag in the US. Unto this day, I still have not seen it in Japan. But then again, I'm not on the look-out, nor have I done any homework!
When I was younger, I was not a fan of tea -- of any sort. Always asked for hot water. They even gave me "sayu" (plain ol' hot water) at the tea ceremonies when I asked. Got to eat the sweetcakes, though! (A child/preteen/teen/young adult always gets preferential treatment!) I even ordered shaved ice with NO syrup! Most places never charged me -- until recently!
Many locals can't partake in caffeine after 3 pm or late afternoon. Houjicha seems to be the answer. Or water -- hot or cold.
Soba-cha (buckwheat tea) has nice aroma and taste. It's my favorite without caffeine in summertime. Yotramas has a good knowledge of tea.
It's true that you only sip a tiny amount of matcha at tea ceremonies. You can't really order a tea of choice, but you might notify to host that you can't take caffeine and sip in form but not drink in actuality, I think.Edited: 8:01 am, March 22, 2013
I love tea but as I get older I'm finding I can tolerate less and less caffeine. Thankfully I have a Japanese friend who comes from a family with a long tea tradition, she is also having to cut back on caffeine consumption but neither of us wish to compromise with our tea drinking. In other words, we prefer to drink something true and complete than a tea that is supposed to be high in caffeine but which has been stripped of many of its qualities through an artificial process. I have had the good fortune to be able to sample a range of low caffeine teas made by Japanese artisans and there are still many wonderful discoveries to be made.
I just discovered this website which offers a powded tea/tisane made with Japanese grown mulberry leaves. There is even a section in English that describes their background.
As mamajelli has graciously confirmed, the interest in low caffeine teas/tisanes may seem like a niche market but that is partly because most of the low caffeinated drinks consumed are just taken for granted - they are what they are, people don't think of a tea they drink regularly as being a low caffeine alternative to tea. Hope that makes sense.
Sorry, this might be a better link to the Kesennuma Mulberry Tea company for English speakers:
Last comment on this (promise!)
This is where I would take you for an uncaffeinated alternative to a "matcha set" at a cafe.
Jibo An Jiyan - Yanaka 5-2-29, near Nippori station (one of my favourite parts of Tokyo)
And here is the kinako latte shown in a blog: