Tough one! I'm a total hypocrite, I wear aftershave from one ex, clothes from a couple of others - actually much of the stuff I own is from a couple of long term girlfriends.
The trick is to keep it in the past. Much stuff is just "stuff", I barely relate my favourite bag to my ex, it's just my bag. I would never tell a new girlfriend about where I got it, it's my personal past and it's staying there.
On the other hand, I used to be really agitated and pissed off when my girlfriend mentioned that certain things reminded her of their old boyfriends... my last girlfriend wore a ring from an ex, and I hated it but never said anything.
I think at some point, either when you grow up a bit or get really serious with someone, you do consider their feelings and either keep your past private or do away with it. If I was your bloke I'd be taking that necklace off, it's almost a massive statement that he's keeping his options open. There's literally nothing wrong if it's just decent jewellery and want to keep it, but if it's related to this promise he's made to his ex, it's plain bad. I'm sure he'd be able to tell her that while they are still friends, he has someone else to think about now and it's silly to hold onto old promises. my best mate wears his ex-girlfriend's hairband around his wrist even though he doesn't want to be with her. I'd say it's just hurtful for the other party, as you're basically saying "I still think about you". Why do that.