The techniques largely depend on the parameters you are interested in - cyclic voltammetry is possibly most common for evaluating the electroactivity of the polymer film. If your polymer is on an optically transparent electrode (e.g. indium-tin oxide on glass / quartz), UV-Vis-NIR spectroscopy or spectroelectrochemical analysis are another commonly used method. If you are interested in the charge carriers present in your polymer film, electron paramagnetic resonance (EPR) spectroscopy is often used (or EPR spectroelectrochemical analysis, if you are interested in the doping / dedoping processes taking place). Conductometry and electroconductometry are also interesting techniques to use, if you are interested in the conductivity of the polymer, particularly as a function of its doping state. Electrochemical impedance Spectroscopy (EIS) and dynamic EIS can also be used for this purpose. More sophisticated techniques can also be used, such as coupled EPR and UV-Vis-NIR spectroelectrochemical analysis (as established by the late prof. Dunsch), depending on the type and amount of information you are interested in. At this point, please forgive me for shamelessly referring to my current project, revolving around combining spectroelectrochemical and conductometric methods for a more "complete" analysis of conducting polymers: https://www.researchgate.net/project/In-situ-ESR-UV-Vis-NIR-spectroelectroconductometry-novel-unique-combination-of-complementary-electrochemical-spectral-and-electrical-techniques-for-an-in-depth-characterisation-of-conducting-polym

If you are interested in film thickness, ellipsometry is a reasonable technique to use. You can also use microscopy, e.g. SEM to evaluate the thickness of the polymer film (usually done when the electrode, on which the film is coated, is broken or cut to show the cross-section). Atomic force microscopy can also be used by repeatedly scanning in the same spot, in order to "scratch away" the soft polymer film and reveal the hard electrode surface, with the film thickness being evaluated by measuring the depth of the groove you have made in the film (in my humble opinion, this is the last resort, as such mechanical stimulation tends to produce wrinkles in the polymer film next to the grove and can make the apparent thickness unreliable). Another approach to measuring the thickness is to use Raman microscopy and do a "deep scan|" (have the focus of the laser keep slowly shifting towards the electrode and record the sequence of Raman spectra; once no polymer signals are observed and electrode signals appear, the thickness is known by the position of the focus). Yet another approach, that we have had little luck with, but supposedly is very reliable is to use a profilometer.

If you want the material characterization, then you should opt for XRD (X-ray diffraction), FTIR (Fourier transform infrared spectroscopy), UV-Visible spectroscopy, XPS (X-ray photo-electron spectroscopy), SEM (Scanning electron microscopy), TEM (Transmission electron microscopy) and many more. For electrochemical characterizations, you can perform cyclic voltammetry (you should know the potential stability window), Charge-discharge (the working current value can be guessed from cyclic voltammetry data), Electrochemical impedance spectroscopy. The above things are just the insight of different characterizations; based on your application, you can perform the required characterization (to be specific).

Others have offered good comments / suggestions to this question, particularly the use of cyclic voltammetry (CV) and electrochemical impedance spectrometry (EIS).

To add a little more, the more important parameter for characterising your conducting polymer coating is the amount of charge passed during the electro-polymerisation process. The thickness of the coating is strongly dependent on the porosity of the polymer coating which is largely affected by the speed of electro-polymerisation and the size and nature of the counter ion, and also the nature of the polymer itself.

The key point is that conducting polymer coatings prepared by electro-polymerisation are all highly porous and mechanically weak. As a result, it is difficult to prepare a very thick coating of conducting polymer (unless a mechanically strong counter ion or dopant is used in the electro-polymerisation process, such as anionised carbon nanotubes or graphenes). This means that measuring the thickness of the coating becomes less important compared with the amount of charge used for electro-polymerisation.

Thank you very much for your answers, they have been very useful to me, I wish you a great success

Best regards.