Understand the terms
A coddled egg is cooked gently, traditionally in a lidded cup or just-below-boiling water. A baked or shirred egg is cracked into a greased ovenproof dish. Recipe names overlap internationally, so the actual heat and container matter more than the label.
Control heat around the dish
For baked eggs, add cream or cooked ingredients if wanted and place the ramekin in a moderate oven. A shallow water bath buffers the heat and produces a gentler set. Hot water should come partway up the dish, not splash into it.
Judge the centre, not the clock
Small changes in dish depth and starting temperature alter timing. Remove the egg when the white no longer looks watery and the yolk has reached the required firmness. The hot dish continues cooking after it leaves the oven.