Microsoft announced a new Azure Connectivity Check as part of the Network Watcher service.  Below is the announcement from Microsoft:
https://azure.microsoft.com/en-us/blog/azure-network-watcher-introduces-connectivity-check-preview/

A couple things to note before you use it:

First, you have to enable your subscription for Network Watcher.  Do this by going into Network Watcher  and selecting your subscription in the Overview blade.  Go to the three dots on the right and enable your subscription.

Next, you will need to install the Network Watcher Agent on the VM you will be testing.  This can be done as a deployment with JSON or with PowerShell.   I users the Set-AzureRmVMExtension method to add the agent to my VM for testing.  Directions for each are outlined here:
https://docs.microsoft.com/en-us/azure/virtual-machines/windows/extensions-nwa

Note that this service is free now, but will be a paid service on October 1st.  The price is reasonable and the service is well worth the money.
https://azure.microsoft.com/en-us/pricing/details/network-watcher/