The Havdalah prayer is comprised of 4 blessings: Wine, Spices, Fire, and Havdalah. However, the middle two blessings are not really part of Havdalah itself, but rather, since the Chachamim wanted people to say those blessings on Motzai Shabbos, they tied it to Havdalah so it could be said over a cup of wine.
However, those are technically self-standing blessings, and while one should try to have all the pieces at once and even postpone Havdalah until later in the night if that's when he'll have all the items needed, one can say Havdalah without a candle, and one could say the blessing on the candle without Havdalah (see Shmiras Shabbos Kehilchasah Vol. 2, 61:17-18).
Note that while this question also would apply to the blessing on spices as well, I'm mainly focusing on the blessing of fire for two reasons: First, if there is some sort of Hefsek issue, it's more likely to occur with the fire, as that generally would be a more involved process to relight. I don't think a smaller Hefsek (i.e. opening the spice jar) would be something that anyone would be Choshesh for, but granted, if you can think of a longer scenario involving the spices, the same question could be asked there. Second, Ma'aseh Shehaya Kach Hava (but of course, for any specific example, CYLOR) ;)
Here's the question:
You're saying Havdalah, and in the middle of the first two blessings, the Havdalah Candle goes out.
Should you relight the Havdalah candle before saying the blessing on the candle, or should you finish the rest of Havdalah, then say the blessing on the candle later separately?
Would you say that once you've started Havdalah, it would be a Hefsek to relight the candle before saying the last blessing (therefore skip that Brachah for now and say it some time later on its' own)? Or would it not be considered a Hefsek to relight the candle?
If you are supposed to relight the candle, does it matter how long it takes to relight it (i.e. the matches were already put away and you'd need to get a new box)?