While in most cases, the resistance would actually be decreasing (e.g. magnetic field-induced charge carriers in conjugated polymers), a material undergoing reorganisation, leading to increased resistance (is your material anisotropic? Perhaps resistance decreases along another axis?) would not be unlikely.
If we are dealing with a thin film, the matter is easier (since we are likely dealing with a well-ordered system, which should be highly anisotropic). Essentially, to evaluate the anisotropy of the electrical resistance, we will need to measure the surface and cross resistance/conductivity of the film. The easiest (and reliable) way to measure surface resistance would be by using the four point probe method (essentially four electrodes in a line, with the outer two enforcing the flow of a constant current and the inner two measuring the potential difference - a very new-user-friendly description can be found here: http://vlab.amrita.edu/?sub=1&brch=282&sim=1512&cnt=1). Cross resistance can be measured using the simplified two point probe technique (electrodes are used simultaneously for enforcing current flow and measuring potential - less accurate), with each electrode touching a different side of the investigated material.
Since your material is a thin film, the question is whether your substrate is conductive (and can be used as one of the electrodes)? If not, can your film be deposited on a conducting substrate?