FIDO2 authentication is starting to be applied in numerous web authentication services, aiming to replace passwords and their known vulnerabilities. However, this new authentication method has not been integrated yet with network authentication systems. In this paper, we introduce FIDO2CAP: FIDO2 Captive-portal Authentication Protocol. Our proposal describes a novel protocol for captive-portal network authentication using FIDO2 authenticators, as security keys and passkeys. For validating our proposal, we have developed a prototype of FIDO2CAP authentication in a mock scenario. Using this prototype, we performed an usability experiment with 15 real users. This work makes the first systematic approach for adapting network authentication to the new authentication paradigm relying on FIDO2 authentication.