The development of cerebrovascular disease is tightly coupled to regional changes in intracranial flow and relative pressure. Image-based assessment using phase contrast magnetic resonance imaging has particular promise for non-invasive full-field mapping of cerebrovascular hemodynamics. However, estimations are complicated by the narrow and tortuous intracranial vasculature, with accurate image-based quantification directly dependent on sufficient spatial resolution. Further, extended scan times are required for high-resolution acquisitions, and most clinical acquisitions are performed at comparably low resolution (>1mm) where biases have been observed with regard to the quantification of both flow and relative pressure. The aim of our study was to develop an approach for quantitative intracranial super-resolution 4D Flow MRI, with effective resolution enhancement achieved by a dedicated deep residual network, and with accurate quantification of functional relative pressures achieved by subsequent physics-informed image processing. To achieve this, our two-step approach was trained and validated in a patient-specific in-silico cohort, showing good accuracy in estimating velocity (relative error: 15.0±0.1%, mean absolute error (MAE): 0.07±0.06m/s, and cosine similarity: 0.99±0.06 at peak velocity) and flow (relative error: 6.6±4.7%, root mean square error (RMSE): 0.56mL/s at peak flow), and with the coupled physics-informed image analysis allowing for maintained recovery of functional relative pressure throughout the circle of Willis (relative error: 11.0±7.3%, RMSE: 0.3±0.2mmHg). Furthermore, the quantitative super-resolution approach is applied to an in-vivo volunteer cohort, effectively generating intracranial flow images at <0.5mm resolution and showing reduced low-resolution bias in relative pressure estimation. Our work thus presents a promising two-step approach to non-invasively quantify cerebrovascular hemodynamics, being applicable to dedicated clinical cohorts in the future.