Spectron is an integration testing framework that's built by the Electron development team (repo, including decent docs):
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Testing your Electron apps with ChromeDriver
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Write Automated Tests for Electron With Spectron, Mocha, and Chai (alternate link)
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Instrumenting Electron Apps for Security Testing
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Spectron questions on Stack Overflow
You can also test Electron applications with Selenium (the Applitools service that blog post is pimping looks pretty cool as well and they have a free trial and an open-source project licensing program). Here's more on Selenium and WebDriver from the Electron site.