I went to japan as a vegetarian and found it almost impossible to eat! which was a shame because it was my first time overseas and was really looking forward to the cuisine. I couldnt even find sushi.
I pretty much only ate soba noodles at the 7/11 (actually tasted pretty good). I tried going around to a few different restaurants with the phrases that rottweiler posted but they honestly look at you like you are crazy, and laugh... not to dishearten you! sorry.
Are you going with a japanese person? or someone who can speak japanese? that would help you a lot.
We had a friend there who took us out to a restaurant one night. He suggested that we have these savoury pancake things (made with egg tho) and while he was trying to order the vegetarian ones, the guy was so confused...it was actually pretty funny. Like, no beef? no. No chicken? no. No pork? no.....No beef?...uh...no...No fish? no. No Chicken? NO!!! then after all that he got out a big bit of lard (still pink) and rubbed it all over the hotplate on the table...we just looked away..we were so hungry! THEN he put dried shrimp on the top!! we picked off the shrimp and ate it anyway. It tasted really good, we just had to turn a blind eye lol
uhhh just re-read that, hope it doesnt put you off...

Japan is amazing I absolutely loved it