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This work considers connected testbeds, i.e., engineering testbeds that are remotely accessible over a network, and focuses on the challenge of achieving a high-fidelity closed-loop integration despite the network delays. To address this challenge, a model-free framework is presented. In previous work, a model-free delay compensation framework with a single design parameter was developed. However, having only one design parameter could limit tuning flexibility and thus delay compensation performance. Furthermore, this framework has not yet been validated on an actual connected testbed. To address these two shortcomings, in this article, this delay compensation framework is first expanded into a two-parameter form, and its open-loop stability and performance are studied for constant delays. The predictor stability criterion is established in terms of the two design parameters and the constant network delay. To evaluate the transient delay compensation performance of this framework and understand its advantages and limitations, simulation case studies are conducted on a connected engine testbed representing a medium-duty diesel pickup truck. These studies include two testbed architectures, constant and variable delays, two drive cycles, two levels of driver aggressiveness, and a comparison against wave transformation as a state-of-the-art benchmark. Finally, the framework is tested experimentally on a physical realization of the same connected testbed. The results validate the robustness of the delay compensation performance of the framework under dynamic operations, and show up to 30% higher integration fidelity due to the additional design degree of freedom introduced through the two-parameter form. [ABSTRACT FROM AUTHOR]