Princess Hisako in a sharp black brimmed hat with pleated teal silk hatband, flowers and beaded triangle (a repeat of her pointed collar, I believe) for the Japanese Orchid & Flower show on Wednesday.
Princess Beatrice spotted on Wednesday in a burgundy velvet padded headband by Isabel Manns
King Carl Gustav and Queen Silvia kicked off the first of 21 visits celebrating the King’s Golden Jubilee this year yesterday to Södermanland County. Queen Silvia wore a cozy faux fur brimmed hat while King Carl Gustav wore a sharp black felt fedora.
This new millinery design caught my eye this week (see the comments for more):
The combination of flora of the four nations of the UK – the rose of England, the thistle of Scotland, the daffodil of Wales and the shamrock of Northern Ireland – to form the shape of St Edward’s Crown on the official coronation logo released yesterday is so fittingly beautiful.
Images from social media as indicated
Royal Hats 
These designs also caught my eye