The Microsoft Connectivity Analyzer tool was updated today. It now includes tooling for testing an Office 365 federated identity provider. This can be used with an Office 365 tenant which is configured for federation with either ADFS or another WS-* based Security Token Service. It can help you to debug issues you have with the federated identity provider with simple tests. The tool is available for download from Microsoft at https://testconnectivity.microsoft.com/?tabid=Client. Once downloaded and run you enter your Office 365 credentials and begin the login test of your federation configuration.
Tests are done from the PC that you download the testing tool to. It will attempt to log in to Office 365 using the federation configuration. The testing will proceed and then show results which should help you to debug federation issues that you may be having.
Here's the result showing that there were errors. You can review the detail to see what the issue is.
The tool is in beta now, so please provide feedback.