Searching indirectly for physics beyond the standard model requires careful investigation of collider data and methodological advances that are the subject of this thesis. In the first part, we develop a multivariate analysis tool to compare data with the new physics prediction in their statistical distributions. The performances are demonstrated through the diboson production process at the Large Hadron Collider, but the method has general applicability. In the second half of the thesis, we study electroweak radiation effects using double log resummation on scattering cross-sections at a future muon collider at 10 TeV or more. We show that these effects play a crucial role in probing new physics, and we make progress towards their complete, accurate evaluation. Both parts of the thesis adopt a general Effective Field Theory description of new physics.