Good quantities of sleep.
That's what leaves me with a clear mind, in the state that I'm able to concentrate.
I studied relaxation techniques and meditation for years way back, and still use them to this day, to make sure that I can function in whatever environment I'm thrown, but, without sufficient sleep (for me, that's about 3 hours to be functional, 5 to be good for most things, and about 7 to really be on form), with it's associated REM sleep and dreams, I don't seem to be quite as sharp as I should be.
One very useful technique for actually solving problems is 'lucid dreaming'. Which is fun once you get used to it.
But, overall, it's the sleep that does it for me:
When I keep going using meditative states, then I'm able to keep going, without most of the side effects of sleep deprivation for several days. However, I don't seem to be able to maintain the longer concentration spans, or the levels of creativity.
Good sleep, and a lack of pressing problems are the best aids I know of for clarity of mind, readying for a good long problem solving session. :)

Malk.