Communication is now a valuable element to demonstrate the degree of commitment and transparency that organizations have towards Sustainability. In a critical moment such that experienced with the COVID-19 crisis, companies recognized facing the challenge of continuous and committed communication on social networks as a sustainable activity. All the latter raises the question whether the brands recognized as the most sustainable have actually succeed on being aware of communicating at the most critical moments of the COVID-19 crisis. In this context, an analysis is made of the activity maintained by the main sustainable companies, both Spanish and Italian, within two of the most popular social networks, Twitter and Instagram, at the very early stages of the crisis in both countries. Our results show that most companies have managed to rise to the occasion and show their commitment to the population through social networks.