Electric grids are undergoing several changes, mostly driven by the replacement of classical highly-inertial generators by converter-interfaced generation and storage systems. This entails the reduction of inherent inertia levels and might lead to instability issues. In a future scenario formed by grids of different natures and characteristics, power electronic converters will play a key role on grid tying applications. These converters are known as interlinking converters (ICs), and they enable total control over the power flow between interconnected grids. Therefore, they are envisioned to take part not only tying hybrid ac/dc systems but also in ac/ac connections. This paper presents a novel control strategy for ICs named dual inertia-emulation (DIE), that improves the dynamic response of tied grids by emulating inertia at both sides of the converter, and which can be employed at any IC regardless of the interconnected grid type (ac or dc). The proposed control is tested by means of time-domain simulations of WSCC 9-bus and IEEE 14-bus benchmark systems. The obtained results demonstrate that the proposed technique increases the equivalent inertial response of the interconnected grids, hence reducing frequency oscillations and the rate of change of frequency (RoCoF), and improving the frequency nadir.