What to do with rounded windows on outside of stuccoed house?

Cut a 4-6” wide circle which will go around the window, a sort of expanded frame. For that matter, check out Archtectural Foam on Google. Many companies do custom. Find out what it would cost For this foam, which should be easier to mount to stucco.

I think it would look great.

You could make a Frame using timber and clad allround OR Just make Sunburst Framework OR Add Hoola Hoops and Pin back to them OR Make it

with a window box underneath and shutters either side to balance.......

Can you just paint it black? That might be striking enough

Would a window box the same color as the window work? Rectangular, but the same overall width as the window. Even a bit of silk ivy. Ivy goes with stucco

It would be lovely to see a photo of the house. Is it Tudor or Spanish Colonial or ?

Could you just do "faux" 1/2 round shutters on either side, so they would look as though if closed, they would cover the window? If you do this in a darker color from a few feet away they would look real and be the most inexpensive fix I can dream up. :) You cold maybe use the rectangle ones you don't like as a basis to create your own stencil out of poster board or cardboard. Perhaps a wrought iron see through look? The window box idea is also a good one no matter what you do on the sides of the window.

Do you want shutters to block out the sun or for decorative purposes? Also, when you say rounded, do you mean the window is round or hexagonal, or that it sticks out like a bay window?

If you are trying to place useable shutters you can build them in the shape of the window and split down the middle. When closed they would just be the shape of the window. When open they would form a half circle/full circle/half circle shape with the arcs of the half circles next to the edges of the full circle. Attach to the house with plaster anchors.

Thanks to everyone for all the ideas. I may incorporate several of them in the project