The externalities produced by high voltage transmission lines are multi-dimensional, may strongly depend on the local context, and are thus difficult to capture through standard environmental valuation exercises. We experiment a GIS approach to design a geographically stratified contingent valuation sample of the population resident in infrastructure corridors in a whole region. We estimate, by means of a binary choice logit model, the perceived marginal damage from impacts of power lines on human health, the landscape and the environment. Specific treatment is given to qualitatively different forms of impact, namely real estate depreciation vs. diffused perception of damage, arising at different distances from the lines. The set of GIS-based variables (proximity to power lines, presence of other infrastructure, endowment of natural and built heritage and other local context variables) prove to be significant predictors in the utility function of resident households. Finally, we compute simulated values that combine information on individual willingness to pay, population density and the dimension of the considered corridor around the infrastructure, so as to generalize the outcomes of case-specific studies for use in policy choices such as infrastructure localization, undergrounding and negotiation of compensations.