Here is a cool tip a lot of my Japanese friends didn't know existed so it might be of help to you as well. Anyway the problem is when you have the default Japanese as an input system on the iPhone you can only input kanji via the keyboard. This can be a problem for some characters you can write but don't know the phonetics for or like me just like drawing kanji. The answer is to add a Chinese handwriting input.
1. open the settings.
2. choose General
3. Choose keyboard
4. choose International Keyboard
5. Scroll down to Chinese
6. I always choose traditional, I am pretty sure simplified should have the same.
7. Turn handwriting on
8. Now open the notepad, here is the English keyboard at the bottom.
9. click the globe on the keyboard for your normal Japanese input.
10. Now click the globe again for handwriting.
11. Draw the kanji you need
12. Select the choice from the right of the screen.
Presto! You have a kanjipad for free!
Why did I figure this out? years building my own kanjipad on Linux