Answer: The Shulchan Aruch (OC 296:6) writes that when reciting havdala one should begin by holding the wine in their right hand and the besamim in their left hand until they reach the beracha on besamim at which point they should switch hands, holding the besamim in their right hand. The Mishna Berura (306:18) explains that as one’s right hand is considered to be more prominent, one should use it to hold mitzva items while reciting the appropriate beracha.
The Aruch Hashulchan (OC 296:17), however, explains that this isn’t strictly necessary as nowadays we place the besamim and candle on the table in front of us. Rather, one should simply hold each one in their right hand as they recite the beracha. Thus, when saying the beracha on besamim¸ one should put the cup down and pick up the besamim. R’ Nosson Gestetner (Lehoros Nosson 8:17) quotes the Beis Yosef (OC 206) who writes that it is sufficient for the cup of wine to be in front of them on the table while reciting kiddush. Likewise, one would not have to specifically hold the besamim or candle, providing they were on the table in front of them. Similarly, R’ Moshe Sternbuch (Teshuvos Vehanhagos 3:92) writes that when the Shulchan Aruch writes that one should hold the wine in one’s left hand, it doesn’t necessarily mean that one cannot put it down.
In conclusion, one should hold the besamim and candle in one’s right hand while reciting the appropriate beracha, though one can put the wine down in front of them while doing so.