Hi Paul,
So, I'm going to make some assumptions here and you can tell me if I'm wrong.
1) I'm assuming that your Portal is federated with your server
2) I'm assuming that you have the Network Analyst license for Server and Portal
You can publish the routing service in 2 main ways, either as a Network Analysis service or as a geoprocessing service that uses Network Analyst. Route, Closest Facility and Service Area analyses can be published as NA services. All of the analyses can be published as geoprocessing services that use NA. Network analysis services—Documentation | ArcGIS Enterprise
See this link for how to publish NA services Tutorial: Publish a network analysis service—Documentation | ArcGIS Enterprise
Check this link for how to publish a geoprocessign service A quick tour of publishing a geoprocessing service—Documentation | ArcGIS Enterprise
If going the geoprocessing service route, you can use the tools in the Network Analyst toolbox->Server toolset to create the models.
Once you have the services published, you'll need to register them with the Portal as utility service. See this link for how to do that Configure utility services—Portal for ArcGIS (10.6) | ArcGIS Enterprise
I hope this helps!
Regards,
Rachel
