Charcoal suit, eggshell shirt,...eggshell tie?

Avoid eggshell period.

Only if you're Regis Philbin

The only place eggshell should be in your closest is covering the walls. A few years back I purchased a beautiful RLPL shirt. The cotton is superfine and it has a great check pattern. Whenever I put it on with a suit it loos off. Its a little better sans tie with a sport coat but still off. It's the awful eggshell background colour that is throwing everything off. It really is a shame and every time I see that shirt sitting in my closest I think about how nice it would be with a plain white background.

I'd like to amend my comment. Eggshell is OK for your business card.

I like ecru shirts (the term usually used for shirts in this colour). Though a pale yellow/cream might be a little better. Now as for the tie, it needs to contrast with the shirt.

White, light blue, cream and ecru are all great shirt colours to wear with a charcoal suit. Pink also works well too, if you're daring enough. And as far as other shirt colours with a suit, I'm not too fond of others, but some people like lilac.