Looks great. I always leave the stems, although do I prune off anything that touches the soil. I'd suggest you build a taller trellis and let that thing go crazy. My cherry tomatoes usually go 9 - 12 feet.

Josh

Oh man! I definitely don't have space for 9-12feet....

tie it up along the railing?

Well, you chose the wrong tomato for that spot :-)
In the future, I'd recommend determinate "Bush" or "patio" or "micro" varieties. Good luck.

Josh

I would let it grow up and over the railing and, as jujustad suggested, tie it to the railing. You could let some branches run horizontally along the fence before going over to hang down. Tomatoes are vines that can grow quite long. I wouldn't recommend cutting "suckers" or branches that have already grown more than 10-12 inches. You're just cutting into your potential yield, and it won't slow down the top growth.

Thanks for the advice guys! Sigh. I admittedly got over excited at the prospect of growing a grafted tomato, that has apparently won all kinds of taste awards. I'm going to have to plan this one better next year! These things better taste good! :-)