The phenomenology of unstable particles, including searches and exclusion limits at the LHC, depends significantly on its lineshape. When the width of the resonance is large with respect to its mass, off-shell effects become relevant and the very same definition of width becomes non trivial. Taking a heavy Higgs boson as an example, we propose a new formulation to describe the lineshape via an effective field theory approach. Our method leads to amplitudes that are gauge invariant, respect unitarity and can appropriately describe the lineshape of broad resonances. The application of the method to the following relevant processes for the LHC phenomenology have been considered: gluon fusion, vector boson scattering and tt¯ production via weak boson fusion.