Do you see a dark blue band in the middle of the picture?

Nikkor 12-24mm f/4 lens @12mm

While many people find that a polariser can help provide dark[er] blue skies, there are limits to what a polariser can do and the filter may not create the effect you want in certain circumstances. Polarisers filter light [and darken blue skies], but they do not do so uniformly – stand with your back to the sun, point your camera to the sky and then turn your polariser ’till the sky is a darker shade of blue and then turn so you are at a 90 degree angle to the sun – you will see the colour of the sky change through your viewfinder as your orientation changes.

If you are using a telephoto or a ‘normal’ length lens [i.e. anything above 50mm], you probably won’t notice these variations in the colour of the sky in your photos – your camera’s angle of view is narrow enough for polarised skies to appear to be a uniform colour.

If you are using a wide or super-wide angle lens however you will have to be careful to make sure your polarised skies do not show this uneven banding – in this case the sky above the boat’s cabin is much more polarised than the sky on the left of the picture. In this case a better way to uniformly darken the sky would have been to use a neutral density filter.