We demonstrate the construction of robust counterfactual explanations for support vector machines (SVM), where the privacy mechanism that publicly releases the classifier guarantees differential privacy. Privacy preservation is essential when dealing with sensitive data, such as in applications within the health domain. In addition, providing explanations for machine learning predictions is an important requirement within so-called high risk applications, as referred to in the EU AI Act. Thus, the innovative aspects of this work correspond to studying the interaction between three desired aspects: accuracy, privacy, and explainability. The SVM classification accuracy is affected by the privacy mechanism through the introduced perturbations in the classifier weights. Consequently, we need to consider a trade-off between accuracy and privacy. In addition, counterfactual explanations, which quantify the smallest changes to selected data instances in order to change their classification, may become not credible when we have data privacy guarantees. Hence, robustness for counterfactual explanations is needed in order to create confidence about the credibility of the explanations. Our demonstrator provides an interactive environment to show the interplay between the considered aspects of accuracy, privacy, and explainability.