Our new house came with a deck and we're already busily planning outdoor dinner parties (at least while the nice weather lasts). We've always been fans of the Candela products' soft, gentle glow. There are no open flames to worry about, and no dripping wax, but the light is similar to a glowing candle.
Our favorite Candela model is this DemiGlow; it's a little smaller and more like a real votive candle glass than the taller standard Candelas. It's cordless and powered by an LED light. It will stay lit for eight hours while remaining cool to the touch. The lights charge up in a base you can leave plugged in and they automatically light up when you lift them out of the base.
If you're going to buy a set, it's more economical to buy multiples; this particular set includes eight DemiGlow lights with rechargeable batteries and charging base.
Related: Outside Cooking: Solar Slow Cooker