In cognitive radio networks (CRNs), the established communication sessions between secondary users (SUs) may be affected or even get interrupted because the SUs need to relinquish the spectrum when the licensed users (PUs) appear and reclaim the spectrum/channel. On detecting the PU activities, the SUs on the affected links either switch to another available spectrum hole using the same link or the SUs seek for an alternative path/link to maintain connection. In either approach, the ongoing session is destined to experience considerable delay or even get interrupted, which is intolerable to quality of service-sensitive applications such as multimedia streaming or audio/video conferencing. In this paper, we study the problem of establishing k-protected routes in CRNs. A k-protected route consists of a set of main links with preassigned backup spectrum and backup paths and is guaranteed to sustain from k PU appearances without being interrupted. For a CRN, we find a k-protected route for each session request and maximize the number of sessions that can be supported. We propose both centralized and distributed k-protected routing algorithms for this problem. Simulation results show that our k-protected routing protocol outperforms existing opportunistic spectrum switching approaches in terms of delay and interruption rate.