Simulation-based testing has been the workhorse of hardware implementation validation. For processors, tandem simulation improves test and debug efficiency by cross-level simulating the Instruction Set Architecture (ISA) and RTL models, and comparing architectural-state variables at the end of each instruction rather than at the end of the whole trace. Further, the simulation may start with the ISA model and switch to the RTL model at some point by transferring the values of the architectural variables, thus speeding up the 'warm-up' phase. However, thus far tandem simulation has been limited to processor designs as other SoC components lack high-level ISA models and thus the notion of instructions. Even for processors, significant manual effort is required in connecting the two models and constructing the necessary controller to synchronize/check/swap between them. This paper leverages the recently proposed Instruction-level Abstractions (ILAs) for generalizing tandem simulation to accelerators. Further, we use the refinement-map that is part of the ILA verification methodology to automate the connection between the ILA and the RTL simulation models for both processors and accelerators. We provide seven case studies to demonstrate the practical applicability of our methodology.