Integrated photonics represents a technology that could greatly improve quantum communication networks in terms of cost, size, scaling, and robustness. A key benchmark for this is to demonstrate their performance in complex quantum networking protocols, such as entanglement swapping between independent photon-pair sources. Here, using time-resolved detection, and two independent and integrated Si$_3$N$_4$ microring resonator photon-pair sources, operating in the CW regime at telecom wavelengths, we obtained spectral purities up to $0.97 pm 0.02$ and a HOM interference visibility between the two sources of $V_{rm HOM}=93.2 pm 1.6,%$. This results in entanglement swapping visibility as high as $91.2 pm 3.4,%$
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