Coplanar waveguide - Calculator question
Scaling all dimensions by the same factor leaves you with the same impedance. However, it does not leave you with the same frequency range. These two are completely independent.

Beware that you have to scale all dimensions. So comparing two coplanar waveguide strips that are (say) 5mm wide and 10mm wide, with proportional gaps, the second one will only have the same impedance as the first if the substrate and the foil thickness double, and the distance to any screen doubles as well. If you keep the same substrate thickess, or foil thickness, then the impedance will shift. If the foil thickness isn't specified, then it's 'thin', and can be neglected in simple models.

In doubling the size, the frequency range over which it works will halve.