I have been growing some herbs in my kitchen in individual pots and they have been growing quite successfully. However, certain herbs, like coriander, have grown to be quite tall, but not strong enough to hold themselves upright. The pots that they are in (that were part of an indoor herb growing kits) have fairly high edges, so I fear this might mean that the plants have had to grow too tall in order to find direct sunlight. Is there anything I should do to stop this? e.g. replanting them in better pots, trimming leaves etc.
In general, stronger light while they are growing will keep them from getting too leggy. Your fear is correct: they are reaching to try to get to the light. This makes them grow too fast and the stems are weak.
I learned a trick from my botany teacher, maybe it can be helpful. There was an indoor container garden using florescent lights and because there wasn't much space for the plants to grow tall, she would pinch off the new growth from the top of the basil plants so that the plant would focus more on filling itself out and having bigger leaves and it wont grow as tall.