In recent years the interest in computational fluid dynamics (CFD)-based analysis of blood flow in coronary arteries has intensified, largely motivated by the possibility of using reliable, comprehensive simulation results as ground truths for training AI systems potentially able to rapidly identify pathologies in hemodynamics. In this paper, we describe very detailed steady-state and transient simulations of coronary blood flow and provide recommendations on appropriate solution methods and parameters for both steady-state and transient simulations. We conclude that when using a finite volume method with polyhedral cells, the characteristic cell size of 0.075 mm is sufficient to obtain a converged, mesh-independent solution for pressure—a variable of interest in many clinically relevant applications such as estimation of the fractional flow reserve (FFR). We also recommend that for transient simulations in coronary arteries, the semi-implicit method for pressure-linked equations (SIMPLE) with 2nd order time stepping be used, with a time step of 1 ms. We suggest that for reliable time-averaged pressure drop results in coronary arteries, six cardiac cycles be simulated, with time averages taken over the last three cycles. The computational effort required for such comprehensive simulations is not prohibitive to generating results for many geometries, with the greatest bottleneck being the extraction of vessel geometries from medical images.