Isolated microgrids have long been considered alternative power system entities that can integrate various types of distributed energy sources such as diesel and renewable power generators including energy storage. Renewable energy sources, such as wind and solar PV, introduce low inertia and high intermittency to the microgrid. For this reason, coordinated control and frequency stabilisation are crucial for maintaining higher service levels in the microgrid. This paper reports on the design and development of two proposed methods for virtual inertia provision, namely model-based and filter-based methods, which support the frequency stability of AC/DC microgrids. The inertial power produced by these methods was implemented through power-controlled voltage source converters, associated with a Li-ion battery energy storage system. To derive and develop the functions for the virtual inertia providers using these methods, a new electromechanical power-speed model was developed to represent the interaction between the microgrid AC/DC-sides and its generators. Small-signal analysis using the linearised form of this model was carried out, in addition to deriving the law for the model-based virtual inertia method. Detailed physical-system simulation and tests were performed, and performance analysis of the resulting generator speed-responses using the proposed methods illustrated their merits compared with other methods, namely the standard df/dt and frequency-event techniques.