Microcavities are key components for integrated optical devices and systems. In this paper, enhancement of the resonance electric field outside a pair of coupled polymeric microcavities of hexagonal shape is investigated. Using numerical simulation, enhancement of outside-cavity field has been demonstrated in different sections of the coupled cavity system depending on particular design. Resonance frequencies are in visible part of electromagnetic spectrum. In reported simulations rigorous models based on solving Maxwell equations for propagating electromagnetic field in polymeric materials commonly used in nano-imprinting lithography is demonstrated.