The only herb I've managed to keep alive and not die a tortuous death inside on a windowsilll is basil. I try and forget about it, look to see if its getting wilted, then toss it a bit of water. Its lasted 3 months so far.
I also get to the end of my scallions (spring onions) from cutting and cooking, then plant the root bearing ends into potting mix in an inside window box, then water them pretty regularly to get them started, then watch them sprout again. You don't get much of a yield, but they do regrow. I keep buying bunches, using them, potting the ends. Gives me what I need in an emergency and the crop rotates. Plus its just fun
Anything else - I kill
But my outside rosemary is finally taking off after a year. I've left it totally alone and it likes it hehe