As in other scenarios, most network authentication systems are based on passwords, which have been widely used during the last decades despite their security vulnerabilities. The WebAuthn standard published in 2019 has described a new authentication paradigm based on public-key authenticators, which are usually hardware devices known as security keys. Although WebAuthn is being used in many web authentication services, security keys have not yet been integrated with network authentication mechanisms. This work successfully developed and integrated a WebAuthn authentication server with a captive portal system, so users can be authenticated using security keys within a web-based captive portal network authentication system. This makes the results presented here are a first approach for adapting network authentication to this new authentication paradigm relying on security keys.