The composite cycle engine (CCE) offers a promising pathway for significantly reducing fuel burn in future aircraft. By integrating a piston system into the core of a gas turbine, the CCE can utilise higher peak cycle temperatures and pressures and thus, achieve a step-change in thermal efficiency. These conditions also promote increased levels of $\mathrm{NO}_x$ formation. This paper presents a methodology for the preliminary estimation of $\mathrm{NO}_x$ emissions within both the piston engine and the subsequent Joule combustor. Fast-responding parametric models capable of capturing key $\mathrm{NO}_x$ sensitivities, particularly the impact of combustion vitiation through water injection and exhaust gas recirculation (EGR), are established. Piston $\mathrm{NO}_x$ is modelled using a two-zone approach, which demonstrates good correlation with reference engine data from literature. For the Joule combustor, a stochastic flow description is employed to predict $\mathrm{NO}_x$ formation, with validation against an in-service combustor confirming the model’s predictive capability. Initial studies indicate high baseline piston $\mathrm{NO}_x$ emissions, though significant mitigation is achievable through water injection or EGR. This work establishes a framework for future research into the emissions and necessary mitigation strategies for the CCE and other advanced combustion technologies.