We use the Lodge Cast Iron Grill / Griddle Plate. For a simmer plate one of the best we have found is the Cast Iron Heat Diffuser by Ilsa.

I now use the All Clad double burner griddle, since I have the grill in my CC. I had the Lodge reversible grill/griddle double burner pan. We used Lodge and Le Creuset for years in our old house, found them a bit heavy over the years. Nordicware and Lodge are better priced over All Clad and Le Creuset. The Lodge and Le Creuset gave my food better grill marks.
I have used an inexpensive simmer plate with a handle and a few octagon shape simmer mats.

Re: Simmer - Do you need a diffuser or an adjustment? From what I've read here, supposedly the CC simmers well when adjusted correctly.

I have both a Lodge and a Staub.

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This post was edited by ctycdm on Sun, Jan 19, 14 at 8:11

and one just fits inside the other making a perfect panini press...;)

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This post was edited by ctycdm on Sun, Jan 19, 14 at 8:12

Thanks for all the responses. In response to the burner adjustment question. The burners all go down very low and I have a small pan burner but sometimes I prefer to use one of the forward burners and they are higher BTU.

Chef King 20 x 14" griddle is what I use. It covers two burners almost completely and it's amazing. I've made breakfasts and tonight just did my first burgers on it. I don't know that I'll ever grill burgers again, they were "restaurant quality" IMO. I also used mine to bake a pizza last night, just swapped it into the oven at 500* for 30 minutes, then turned on the broiler. I made a 14" pie in 4 minutes and some change and it was incredible. It won't do grill marks but those are for decoration IMO, the more you can brown/sear the outside, the better, regardless of the protein you're cooking.

I just looked at the lodge double pro and the single grill/griddle. The 20" dimension on the double doesn't seem like it will fit across 2 burners properly. The raised edge looks like it will make it rest above the grate. The single looks like it will fit right over the top of the grate. Which models are people using on the CC and how well do they fit. Thanks.

Chef King Griddle 14"x23" RN1423-8 is what I use on my Capital Culinarian CGRT366. Heavy duty and high quality, works very well. It fits perfectly. About the only negative, it's heavy 17lbs.

This post was edited by DJ493 on Thu, Jan 23, 14 at 10:55

Thanks for the tips on griddles. I'm going to theg the Chef King 14x28.

Chef King is the one. I made a grilled cheese, turkey, and tomato on ours today.
Billy

Billy - you are making me hungry!