In reply to Bertbee:
This massively depends on what you are climbing. For something short and single pitch, then there really is no issue. If your second can't follow, just either ab off to get the gear (doesn't take long once you are slick) or get her to haul up on some gear as you haul up on the rope to pass a difficult bit. Abseiling is simple to rig with practice, and a simple prussic to protect yourself (and a wrap of the rope around your leg when you want to stop for a while) will protect you. Gear to the side or short traverses are really not a problem to clean.
If you get stuck halfway, then you'll just have to lower off some gear and either leave it or ab for it.
Multipitch is a bit different, and I have to admit that I wouldn't start up anything that I knew would be beyond my partner unless they were happy to use ascenders (which is tiring and dull).
My one piece of advice is to push things rather than acquiesce to your partner. I spent many years in Sheffield climbing harder than many of my partners, and I would very often just have easy days out. They were all fun, but I now feel that I could have done a lot more. If you are only doing one harder route in a day, it doesn't really amount to a large degree of selfishness and shouldn't take too much time. And you might find that your partner enjoys having a crack at some harder stuff too.