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
As David Makogon's answer points out, applying an IP-based SSL certificate only gives the website a static inbound IP address.
However, the outbound IP address a website uses when making outbound network calls can be determined based on where your website is hosted. Microsoft has a list of the these IP addresses here. The third-party service would have to whitelist all of the IP addresses used by the scale unit your website is hosted in (e.g. waws-prod-am2-005).