Buildings rarely perform as designed/simulated and and there are numerous tangible benefits if this gap is reconciled. A new scientific yet pragmatic methodology - called Enhanced Parameter Estimation (EPE) - is proposed that allows physically relevant parameter estimation rather than a blind force-fit to energy use data. It calibrates a rapidly and inexpensively created simulation model of the building in two stages: (a) building shell calibration with the HVAC system is replaced by an by an ideal system that meets the loads. EPE identifies a small number of high-level heat flows in the energy balance, calculates them with specifically tailored individual driving functions, introduces physically significant parameters to best accomplish energy balance, and, estimates the parameters and their uncertainty bounds. Calibration is thus done with corrective heat flows without any arbitrary tuning of input parameters, (b) HVAC system calibration with the building shell replaced by a box with only process loads; as many parameters as the data allows are estimated. Calibration accuracy is enhanced by machine learning of the residual errors. The EPE methodology is demonstrated through: a synthetic building and one an actual 75,000 Sq.Ft. building in Pennsylvania. A subsequent paper will provide further details and applications.