DTLS is a protocol that provides security guarantees to Internet communications. It can operate on top of both TCP and UDP transport protocols. Thus, it is particularly suited for peer-to-peer and distributed multimedia applications. The same holds if the endpoints are mobile devices. In this scenario, mechanisms are needed to surmount possible network disconnections, often arising due to the mobility or the scarce resources of devices, that can jeopardize the quality of the communications. Session resumption is thus a main issue to deal with. To this aim, we propose a fast reconnection scheme that employs non-connected sockets to quickly resume DTLS communication sessions. The proposed scheme is assessed in a performance evaluation that confirms its viability.