Tenssaiga
One would think that after recognizing your once love whom you were torn away from, you would try to get things going again, but we're assuming that Sesshoumaru had no such logic. Besides, everyone knows that you should bend reality so that things would go the way you want them to. So now we have Sesshoumaru and Kikyou falling in love with each other all over again.
Everyone knows that there's no such thing as a developing relationship. Well, there is, but it goes from strangers to friends to lovers. There is nothing between any of these steps.
Therefore, following such perfectly sensible logic, Kikyou started acting like a moron in front of Sesshoumaru because she was in love (right after their best friend thing during the telling of sob stories). Most people, or rather, normal people, try to get to know someone well before falling in love. However, Kikyou figured that exchanging sob stories served well enough as getting to know someone.
She would stutter and blush around him. Technically, that would be considered a crush. When you love someone, you're usually supposed to be comfortable around them (but hey, what do real people know about emotions?). As for Sesshoumaru, he was acting the same, but found himself constantly staring and forgetting his manners. Or perhaps he was just never taught.
Like Inuyasha and Kagome' relationship, it didn't really progress. They blushed, stuttered, stared, had their hearts pounding, and did a whole lot of other stupid, lovesick stuff. And yet, nothing happened at all. It builds suspense and makes the reader wonder what'll happen, because obviously no one could ever possibly imagine that the two would wind up together.
While in their awkward dance of a crush mistaken for true love, they decided to tell sob stories again. This time, Kikyou whined mostly about how she was dead. Personally, I think it would be nice to remain young forever and not die even after falling off cliffs three times. But then Kikyou started lecturing on psychology and how something cannot be valued if it cannot be taken away (in reference to her life). So Sesshoumaru, out of his great love for her (or rather, more plausibly, he just got sick and tired of her complaining), offered to revive her using the Tenssaiga. Kikyou agreed.
So Sesshoumaru revived her and she got a soul back. However, the story at this moment does not mention anything about Kagome, who was in possession of Kikyou's soul. Therefore, we will assume that one of Tenssaiga's unknown abilities is to duplicate souls in order to avoid yet another plothole.
Next comes the teary moment where Kikyou starts crying again and Sesshoumaru is completely bewildered because he does not understand the concept of crying from joy. We have this cute little moment where Kikyou is thanking him and she gives a whole long speech that sounds oddly familiar to award-winning speeches during the "I could not have done this without..." section.
Because Kikyou was revived, the two suddenly managed to pull together the courage to tell each other what they felt. So either one of them kissed the other and they started making out. They were completely oblivious to the fact that they were in the feudal era, back when you don't kiss someone until after you're married. So let's just say that Kikyou was a slut and Sesshoumaru was a pervert like Miroku to avoid a plothole.
After kissing for five to ten minutes, they had to part for breath, even though if they hadn't been breathing for five minutes, they probably would've died by now. But hey, this is fiction; that means not real, so whatever outlandish, lack of common sense things the writer wants can happen.
Being the completely uncreative people that they were, Kikyou and Sesshoumaru said the two most cliched line known in romance novels:
"I love you."
"I love you too."
Then, they started making out again.