Say you've calculated that a piece sacrifice gives you a good attack, say for example a Bxh6. It is however not clear for both players whether the sacrifice is sound or not. - Then your opponents declines your offer and plays an other move. I usually am disappointed. I foresaw some interesting stuff, but my opponent won't have anything of it. Or should I in that case be content with the extra pawn won?

Or should I in that case be content with the extra pawn won? - that is.

I always thought snagging extra material was a worthwhile result.  But I could be wrong.

It might be the case that your opponent has seen a better counter-attacking line than simply accepting your sac... so, when your opponent declines, it might be a good time to see if he has a counter-punching continuation that you didn't see before. 

On the other hand, if might be that your opponent is declining because he thinks that your sac is sound, and is allowing you to keep the material you've gained so that he can defend more effectively... in which case, congratulations, you've won a pawn (or whatever).

Be content with the free material

When I sacrifice pieces I play for the mate, not for the winning of a pawn :-p. I'd be too much disappointed to not have witnessed the soundness of the offer to enjoy the extra material. @Ericdodson. True, many a times I got badly beaten by counterattacks, but that is all good because I learned from that when I should or should not consider to sacrifice. But just declining by making a solid, safe move does not test it as i wished it were

@TeraHammer: yeah but the point is it wasn't a sac because the opponent didn't take it.  So not knowing the position, I assume our protagonist won a piece and moved out of the sac position?  

@fbhjr. That depends all on the position and whether or not I still see something good happening letting the offer stand or not.

@teraHammer: yes indeed.  I wish the OP would have posted the game.

I'd rather not turn this discussion into a discussion if my sac at that point was sound or not, but I want to know how other players feel when their interesting sacrifices are declined.

Well I feel like crap, because usually the sacrifice is the first move in a great idea, and when it is declined, I'm befuddled and out of ideas (unless I can snag some material).  I have had a few recent games in which my offered sac was declined, and I just thought opponent knew what I was doing.  So, yes, it made me feel deflated.  

My personal feeling is that if a sac gains an advantage or wins a game only if my opponent happens to accept it, well, it's not really such a brilliant idea in the first place -- no matter how clever it may seem otherwise.  If a sac works only when it's accepted and not otherwise, then it's more on the order of a gimmick or a swindle rather than an actual brilliancy.  But hey, that may be just me.  Your results may vary.  Offer void where prohibited.   

True. Maybe better put, the sac is then nothing but a trap. "Free piece, come on, take it!" ;-D. Ideas behind unforced traps are good to consider however for future combinations when sacs are more forced :-D