Both my grandmothers died years ago. My maternal grandma died from cancer when I was just shy of 14 and my paternal grandma died when I was 15. Those two deaths made me realise how differently you can feel towards relatives. The maternal grandmother had been the typical granny, so I was quite taken aback when she died. The circumstances were rather tragic (not "nasty" though) as well. My paternal grandmother however was, as is my father, fairly old so I only ever really knew her as an old frail lady who wasn't really active anymore.
One thing you should do, if you had a good relationship with your grandparents, is selecting good memories. There's no use in dwelling on some stupid little quarrel you had ten years ago, wishing things had gone a different way. Love is stronger than death, and good memories are the foundation for love.
Oh, and after the hearty bit, I'll of course offer you my condolences.
[Edited 2007-05-18 23:19:48]
Don't cry because it's over, smile because it happened.