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There has been a recent increase in efforts to develop broader models to assess the impact of climate change and climate change policies, both in terms of impact measures (beyond GDP) and in terms of modelling complexity (beyond DICE/RICE models). Climate policies aimed at reducing CO2 emissions can have impacts in multiple sectors of the economy, and can change consumption levels over time. We show how the sustainability indicator Genuine Savings can be endogenised within a general equilibrium model and used as a criterion for judging the impacts of such policies in terms of future well-being. Differences in Genuine Savings rates between CO2 emission reduction scenarios are discussed. We show how a broader, Genuine Savings-based assessment of climate change can result in a re-evaluation of the consequences and costs of inaction in terms of various climate change-related policies; and how multiple environmental and well-being outcomes can be analysed within a unified modelling framework.