You don’t need to light a candle to say a novena. It’s common, and it’s an ancient Christian practice, to light candles before praying and leave them burning afterwards. (St. Jerome talks about little old Roman Christian ladies doing it in his day. And it’s particularly interesting because Romans commonly used oil lamps for light. Candles were a Northern European thing, just like they drank beer and used butter while Italians drank wine and used olive oil.)
Early Christians tended to remind themselves to “keep watch” as Jesus commanded, by praying all night on special holy days, or at least for parts of the night. Candles and prayer may also have become associated by the ancient Jewish and Christian custom of singing Psalms and hymns as a household at the time of night when one lit the oil lamps (we’d say, the time we have to turn the lights on). We don’t know much about the beginning of it; it’s just that old a thing.
Anyhoo…
If you’ve got one of those big glass jar votive candles, they’re supposed to last a long time, something like six to nine hours. So yes, I’d say that you should either blow them out after you are finished praying, or only let them burn for a short time more.
However, it’s pretty common to leave candles burning on the windowsill or another safe place, as a sort of continuation of your prayer, just like you’d do with a votive candle in church. Many people find it very peaceful to keep a prayer candle going.
(Assuming you make sure to keep an eye on it, no drapes or flammable stuff around it, no cats jumping up and knocking it down.)
So it’s your choice. Do what seems right to you. Experiment. Maybe burn the candle for a half hour or an hour?