The significant carbon footprint of the ICT sector calls for methodologies to contain carbon emissions of running software. This article proposes a novel framework for implementing, configuring and assessing carbon-aware interactive software services. First, we propose a methodology to implement carbon-aware services leveraging the Strategy design pattern to feature alternative service versions with different energy consumption. Then, we devise a bilevel optimisation scheme to configure which version to use at different times of the day, based on forecasts of carbon intensity and service requests, pursuing the two-fold goal of minimising carbon emissions and maintaining average output quality above a desired set-point. Last, an open-source prototype of such optimisation scheme is used to configure a software service implemented as per our methodology and assessed against traditional non-adaptive implementations of the same service. Results show the capability of our framework to control the average quality of output results of carbon-aware services and to reduce carbon emissions from 8% to 50%.