Using Molecular Dynamics Simulations, We Study the Role of Finite Size Effects on the Determination of Interfacial Thermal Resistance between Two Solids Characterized by High Phonon Mean Free Paths. in Particular, We Will Show that a Direct, Heat Source-Sink Method Leads to Strong Size Effect, Associated with Ballistic Phonon Transport to and From, and Specular Reflections at the Simulation Domain Boundary. Lack of Proper Account for These Effects Can Lead to Incorrect Predictions About the Role of Interfacial Bonding and Structure on Interfacial Thermal Resistance. We Also Show that the Finite Size Effect Can Be Dramatically Reduced by Introduction of Rough External Boundaries Leading to Diffuse Phonon Scattering, as Explicitly Demonstrated by Phonon Wave-Packet Simulations. Finally, We Demonstrate that When Careful Considerations Are Given to the Effects Associated with the Finite Heat Capacity of the Simulation Domains and Phonon Scattering from the External Surfaces, a Size-Independent Interfacial Resistance Can Be Properly Extracted from the Time Integral of the Correlation Function of Heat Power Across the Interface. Our Work Demonstrates that Reliable and Consistent Values of the Interfacial Thermal Resistance Can Be Obtained by Equilibrium and Nonequilibrium Methods with a Relatively Small Computational Cost. © 2014 American Physical Society.