"but, it seems we would need to continue to use the vCenter 4 license until after the migration of all the ESXi hosts to vCenter 5.1 is complete"
Here you have set up a new server for vcenter 5.1 once you are done with all settings add license to the new vcenter server 5.1. Now you have two vcenter servers (vcenter 4 and vcenter 5.1). Then disconnect the hosts one by one from vcenter 4 and connect them to vcenter 5.1. Since we have two seperate vcenter servers here so no need to worry about licensing here. Once you complete all migrations, you can decomm the vcenter 4 server.
regarding ESXi licenses:
You can use single license key for multiple ESXi hosts provided only the CPU count matters there, if you have license key for 6 CPUs and you have added only one host using that license, if you have assigned license for 2 CPUs remaining 4 will be unused and you can use that any time, it is not mandatory to add all hosts at same time. There are scenarios where customer purchase licenses for 100 CPUs but not necessary to use all at a time and we can use whenever required.