I would like to put the UK Royal Shield of Arms coins in my binder by making a custom coin sheet myself so as to display them like this :
How would you do to make something nice and clean ?
I am no DIY expert but I would suggest getting a piece of cardboard; folding it in half, stapling a plastic sheet in the middle (so it looks like a giant 2x2 cardboard flip) and then cutting holes for each of the coins in the cardboard. After you insert the coins you can staple around the holes to hold them still.
If you got one of those printed you could cut a frame from cardboard and seal it in plastic yourself. It's flat enough that it would all fit in one of those full sized sheets. It could go in your binder that way.