I\'ve been trying to find an answer to this for a few days.
I want to host a new azure website in either the Basic tier or Standard tie
An SSL cert with Web Sites will be tied to an inbound IP address. However, Web Sites does not provide a static outbound IP address.
If you need a static IP address to align with 3rd-party services, you'd need to have something residing in Azure (e.g. Application tier) running in a cloud service / VM that your web site accesses, and then have that app tier (with static IP address) communicate with your 3rd-party services.