If you know the refractive index of the material in its dense 'phase', you can get an estimation of the refractive indices of your films by spectrophotometry and/or ellipsometry, and estimate the 'packing density' of the film from the indices.

It depends on what you want to know.  Electron microscopy will be excellent to characterize the pore dimensions, and you could get an idea of the coatings' overall porosity through counting methods.  Another option is impedance spectroscopy.  This would yield no information on individual pores, but is very good an obtaining the macroscopic porosity of the entire coating.

By AFM analysis. or porosity can be analyzed with an optical profilometer.

Use BET to assess pore distribution and porosity following this model:

http://www.rsc.org/suppdata/lc/b8/b812301b/b812301b.pdf

It will give you a much better outcome and be more systematic than EM - although I would suggest to do both to back yourself up. Also make cross sections with FIB and look at them to assess the amount of through pores if any.

If you know the refractive index of the material in its dense 'phase', you can get an estimation of the refractive indices of your films by spectrophotometry and/or ellipsometry, and estimate the 'packing density' of the film from the indices.

Agree with Daniel, we used fitted ellipsometrical data and the theoretical refractive index to estimate porosity by using Yoldas mixing rule. See for example Tamar et al., Sol.Energy Mater. Sol. Cells 130 (2014) 246-256

Maybe you could also think about small angle x-ray or neutron scattering technique (SAXS and SANS). As far as I know, these are also applied to characterize porosity, pore size distribution, etc.

Agree with Daniel Poitras and Roman Kubrin. We also used refractive index data obtained by spectrophotometric measurements and Bruggeman effective medium approximation for calculation of packing density and free volume fraction. The problem  of these calculations is that you can not distinguish between opened and closed porosity because what you have determined is the overall porosity. Good option is the ellipsometric porosimetry where someone measures the "empty" sample than fill it with water vapors and measure again its 'filled' state. The difference is the open porosity. I have never used it. If some one can do this for me I will be very gratefull.

There's an empirical expression in the attached paper for estimating coating porosity by electrochemical methods. 

Also, try B. Matthes, E. Brozeit et al., Surf. Coat. Technol. 49 (1991) 489.

Thank you very much for all your responses. I found some interesting ideas and hope, that I will use them in the future.