Mitigating climate change requires a portfolio of strategies and the use of carbon dioxide removal techniques or negative emissions technologies (NETs) will be necessary to achieve to achieve this goal. However, the high implementation costs of advanced NETs lead to expensive carbon credits, hindering their broad acceptance and use. One potential solution involves governmental support through subsidies, aiming to boost the availability of NET-derived carbon credits. This research uses a graphical technique based on an extension of pinch analysis to identify the ideal subsidy level for carbon dioxide removal, taking into account factors such as carbon pricing, supply, and demand. The proposed approach modifies the limiting composite curve (LCC) methodology to accurately determine the optimal subsidy and establish the baseline amount of subsidized carbon dioxide removal needed. The approach enables the convenient and efficient construction of the LCC using a composite table algorithm. To illustrate the proposed methodology, two case studies composed of different NETs and demand sectors are investigated. The results show the most advantageous subsidy levels for these technologies, providing valuable insights to guide policymakers and investors in their decarbonization efforts. This research contributes to the development of effective governance and investment strategies by optimizing NET subsidy allocation. Such optimization is crucial for facilitating the widespread implementation of these technologies, which are in-line with the global efforts to mitigate climate change.