The theanine high is the main reason I drink tea. I've experimented with many kinds of tea, although I haven't tried matcha yet. I get the best high from Gyokuro and Silver Needle White. Regarding the Silver Needle White, it's important to get good quality. The leaves should be whole and well formed and you should be able to see the silver down which covers each leaf.
Also, to get the best high, proper brewing is essential. Theanine will dissolve in water temperatures above 120 degrees F (50 C). Caffeine and the more bitter tannins tend to dissolve at higher temperatures. If the water temperature is above 176 degrees (80 C), the bitter tannins and caffeine will overcome the Theanine, masking both the taste and the mind altering effect. So, the secret of getting the natural ‘high’ of tea, along with a sweeter and less bitter taste, is to brew the tea with cooler water, ideally between 150 and 160 degrees.
For Silver Needle, I use a heaping tablespoon to 10 ounces of 160 degree water. I let it brew for 12 to 15 minutes with a lid on the cup. I know that may seem too long, but at this temperature, it's ok. It won't taste bitter. After 15 minutes, you'll have a golden liquor, the perfect temperature to drink.
The Gyokuro must be brewed with even cooler water, ideally, about 150 degrees and not more than 2 minutes. I use a level teaspoon to 10 ounces of water. With both varieties, a second brewing is fine. But most of the theanine is exhausted after the first brewing. So, for the second brewing, I use less and slightly hotter water, producing maybe 5 ounces of tea that has a higher caffeine content.