Structural health monitoring (SHM) plays an important role in maintaining system integrity of aging structures and machinery parts. Microelectromechanical system (MEMS) accelerometers, because of their low cost and small dimensions, have emerged as attractive sensing tools for monitoring structural condition based on changes in structural vibration characteristics. For SHM applications, these sensors need to detect low-amplitude and low-frequency vibrations (microvibrations). Those are not always feasible with the conventional low-cost digital sensor boards. In this paper, a novel accelerometer board, named acceleration evaluator (ALE), is developed to achieve more accurate wireless vibration measurements using the full bandwidth of the installed MEMS accelerometer by a voltage-to-frequency converter, instead of the conventional analog-to-digital converter. The effectiveness of the prototype is evaluated through laboratory tests, demonstrating its measurement accuracy comparable to that of wire-based integral electronics piezoelectric accelerometers. Furthermore, ALE performance for SHM purposes is validated by carrying out shaking table tests on the real-size model of a stone pinnacle of the Washington D.C. National Cathedral.