I just stopped at a garage sale and a guy had the following:
Custom 57 cm road bike with shimano tri-color... he said the frame builder was engineering student at the university of Wyoming. It was extremely light and road very nice. He was asking $450... any idea what it would be worth... hard to say in my opinion since the frame builder is unknown.
I liked the frame... but I only took it for a short ride. Now that I look at the pictures... I see what our saying that top tup is crazy long. The guy said he raced it and road a few triatholons on it. He wants to throw in a box of jerseys, padded shorts, a few tires, some aero bars, old bike shoes, and a shimano ultegra front wheel.... all for the $450 price.
Parts its worth about $200 to me but I figured that would be an insulting offer.
That was kind of my feeling. It road nice... but I"m not going to bother with it... it has some sentimental value to the guy so I don't want to insult him by offering him less than half what he wants for it.
2012 Cinelli Saetta, vintage steel cougar, Kona Jake
Sentimental value is worth nothing to you, if you want it, offer what you think is fair, and don't worry about insulting them. Why should something that means something to them mean anything to you? The bike is only worth what somebody is willing to pay.
Dealing with used toys, cash is king. I went with a friend who wanted a road bike, I found her a '87(?) Celeste Bianchi Limited with Columbus Steel and Shimano 600 parts (105 shifters), they asked $400 for it, and told us another buyer was interested in it sight unseen and was willing to pay $420 for it. She was only willing to pay $350, we just said we're here, and here's what we'll pay. Guess who got the bike? This bike too had a ton of sentimental value, wife spent 20 minutes saying goodbye to the bike.
Just remember, you have no attachment to their stuff and they may have a history with their stuff, but they're willing to get rid of it, so it doesn't really mean all that much to them if space is more important to them.