A cost or resistance surface is a representation of a landscape’s permeability to animal movement or gene flow and is a tool for measuring functional connectivity in landscape ecology and genetics studies. Parameterizing cost surfaces by assigning weights to different landscape elements has been challenging however, because true costs are rarely known; thus, expert opinion is often used to derive relative weights. Assigning weights would be made easier if the sensitivity of different landscape resistance estimates to relative costs was known. We carried out a sensitivity analysis of three methods to parameterize a cost surface and two models of landscape permeability: least cost path and effective resistance. We found two qualitatively different responses to varying cost weights: linear and asymptotic changes. The most sensitive models (i.e. those leading to linear change) were accumulated least cost and effective resistance estimates on a surface coded as resistance (i.e. where high-quality elements were held constant at a low-value, and low-quality elements were varied at higher values). All other cost surface scenarios led to asymptotic change. Developing a cost surface that produces a linear response of landscape resistance estimates to cost weight variation will improve the accuracy of functional connectivity estimates, especially when cost weights are selected through statistical model fitting procedures. On the other hand, for studies where cost weights are unknown and model selection is not being used, methods where resistance estimates vary asymptotically with cost weights may be more appropriate, because of their relative insensitivity to parameterization.