If I understand the question correctly, you are wanting to use the same public IPs across both ISPs. Just routing to one or the other router (as the answer suggests) will not work because both ISPs will be giving you different address space.

Your best bet in this case if you’re a small organization and don’t have IP space or can’t peer with your ISPs is to just route out your primary connection normally and then have secondary DNS entries etc if you’re dealing with mail and such for your second connection.

To explain further. ISP A assigns you address x.x.x.x ISP B assigns you address y.y.y.y. Even if for some reason in a failover situation ISP B would accept the x.x.x.x address space for outbound requests, return traffic would still attempt to travel through ISP A. Basically what you would be doing to account for this is create a dns entry that would say to reach mail1.myorg.com use x.x.x.x. The next entry would be something like mail2.myorg.com. then each router would nat to its ISPs address space.

Or if the servers are in a DMZ then you would only set up NAT for the failover connection. It really just depends on your topology.

Anyways that is just one scenario, there could be hundreds I’m sure depending on how you’re set up but I hope that helped you get an idea of a direction to go.