I had to go through this with both of my children when I stopped breastfeeding. They wanted feeding to sleep and feeding again if they awoke in the night. They were both 14 months so probably a lot older than those you are talking about but also more set in their ways and so the habit was harder to break.
I left them crying for 5 minutes, then 10 and then for a maximum of 15. When I went in I did lift them and gave them a cuddle til they calmed down. They tended to calm quickly once lifted and then I put them back down straight away and left the room. I never spoke the whole time - just gave the minimal amount of comfort to calm them down.
It took a week with my youngest child. The first few nights it would take half an hour, both to settle him to bed in the first place and when he woke up at night. Then it lessened to around half of that and by a week he was sleeping through - at least as far as I was concerned, because if he did wake up I wasn't aware of it as he just went back to sleep. I think it may have been this easy with him because he wasn't as much in the habit of feeding to sleep - he would let go of the nipple before he actually dropped off whereas my eldest would wake up as soon as the nipple fell from his mouth!
The eldest boy was the hardest experience with this method. It took a month. For the first three nights it took an hour to settle him each time. When he first went to bed and then twice through the night. He cried until he was sick for each session of the first night and the first session of the second and third night. I stood his cot on an old quilt and had a change of bedclothes ready. When he was sick I went in, did a quick change of bed and nightclothes, cuddled him and calmed him and carried right on with the routine - leaving him with as minimal fuss as possible.
After the first three days he stopped crying til he was sick (at that age I could see he was forcing himself to be sick so I guess he gave up on that one as it didn't work). However, I still had to carry on with the routine for an hour at a time for the rest of that first week. The next three weeks the time he was up got shorter and shorter until after a month he was finally going to sleep without a feed and going back to sleep if he woke up. I really do think it was this hard with him because of the attachment he had to breastfeeding to send him off to sleep.
I also think it may have been harder with my two because I was weaning them off both breastfeeding and waking during the night at once. I had to because it was the fact they expected a breastfeed that kept them awake. At the age they were, your body really doesn't want to continue being woken up during the night and I was finding it really hard to cope, so it had to be done.
It was hard, especially the throwing up part, but it was definitely worth it. I really appreciated the full nights sleep I got when it worked. I did have a relapse with the eldest boy when he was ill for three weeks once and I was so tired dealing with him through the night that I ended up letting him sleep with me for a week. This caused a relapse of a week, including the throwing up again for the first night, which had to be handled again in the same way and was again successful though in a quarter of the time.
My sister had the same problem with her son and couldn't handle this method. He slept with her all the time until he was 5. She never got a decent nights sleep as he was a restless sleeper. It caused problems between her and hubby too for obvious reasons. He's 8 in August and still sleeps with her for quite a lot of the time. This makes me so glad I stuck to my guns!
Good luck with whichever way you go.