Since the discovery of the Higgs boson at the CERN LHC, the hunt for new physics - new particles that are not predicted in the standard model (SM) of particle physics - has continued. In parallel, increasingly precise measurements of the Higgs boson and other SM particles are being performed. So far, this search for new physics has not led to a discovery. It is therefore important to consider the possibility that the new particles we are looking for are heavier than can be produced at the LHC. In this case, it is only through precise measurements of the Higgs boson, and other SM particles, that we can learn about the presence of new physics, and so this avenue must be explored. In this project, we propose to develop a new method to perform measurements of the Higgs and electroweak sectors at the LHC, to be as sensitive as possible to the effects from new physics whilst providing sufficient information for the results of a measurement to be included in a global combination of measurements, which provides the best constraints on the presence of new physics. The novel measurement approach will be demonstrated through a measurement of Higgs bosons and Z bosons, paving the way for wider adoption of this method.