With all the changes moving to ASP.NET Core, I am not quite sure where Katana fell in the process, so apologies if this has been answered previously.
Previously, we could host Katana in a Console Application or Class Library. However, since Katana has been integrated into ASP.NET, it seems increasingly unlikely we will see UWP support for Microsoft.Owin.
Given that, is there another method of using OWIN for hosting web services (i.e. Web API or Nancy) in a UWP application?
With all the changes moving to ASP.NET Core
Ref Introduction to ASP.NET Core
ASP.NET Core is a new open-source and cross-platform framework for building modern cloud based internet connected applications, such as web apps, IoT apps and mobile backends
You can develop and run your ASP.NET Core apps cross-platform on Windows, Mac and Linux.
is there another method of using OWIN for hosting web services
This is an unreasonable requirement, UWP app is not appropriate to host server-side Web service. If you see the App lifecycle, you will find the App execution state may block the service logic operation if the app hosts a service.
If we need to provide services to other UWP apps, creating and consuming an app service is the right direction: Create and consume an app service