The Shulchan Aruch (OC 624:3) writes that one does not use besamim for havdala following Yom Kippur even when Yom Kippur falls on a Shabbos. The Mishna Berura (624:5) explains that we usually smell besamim to console us over the loss of our neshama yeseira, extra soul, that departed at the conclusion of Shabbos. As we are fasting on Yom Kippur, we don’t have this neshama yeseira and so don’t need the besamim.
The Mishna Berura (297:2) points out, however, that if one were fasting on another Shabbos, one would still use besamim.
The Magen Avraham (OC 624:1) and Taz (OC 624:2) disagree writing that as one benefits from the pleasant aroma, it can’t be considered a bracha l’vatala. Similarly, other poskim write that there is always a neshama yeseira present on Shabbos and so one should use besamim (See Aruch Hashulchan OC 624:1).
The Kaf Hachaim (OC 624:9) suggests that one should rather recite the bracha of besamim after havdala.
We light a candle in havdala following Shabbos to commemorate its creation and discovery by Adam (Pesachim 54a). We light a candle after Yom Kippur, however, to demonstrate that the light which was forbidden on Yom Kippur may now be lit (Mishna Berura 624:7).
To highlight this point, rather than create a new flame, one should use a light that had remained lit throughout Yom Kippur. One may light another candle from this one and hold them together for havdala.
The Magen Avraham (OC 624:7) writes that this applies, too, when Yom Kippur falls on Shabbos.R’ Moshe Feinstein (Igros Moshe 4:122) writes that if one doesn’t have an existing flame following Yom Kippur, one should do so without reciting the bracha. When Yom Kippur falls on Shabbos, however, one may recite the bracha even on a new flame (Yalkut Yosef, Moadim p116).