Intermediate-scale quantum devices are becoming more reliable and may soon be harnessed to solve useful computational tasks. At the same time, common classical methods used to verify their computational output become intractable due to a prohibitive scaling of required resources with system size. Inspired by recent experimental progress, here we describe and analyze efficient cross-platform verification protocols for quantum states and show how these can be used to verify computations. We focus on the pairwise comparison between distant nodes of a quantum network, identify the most promising protocols, and discuss possible implementations in laboratory settings. As a proof of principle, we implement basic versions of these schemes on available quantum processors.