Yes, metal is floating in my example that you showed. The effect of that metal on Q factor shown there is an eddy current flowing around the cutout, and no port is required to show/model this.
If you want to put the ground plane at defined voltage, or model a patterned ground shield underneat the inductor, you can place a single port there. All ports, inductor and metal shield, can keep their ground reference at default global ground = bottom of the substrate. This way, you can still evaluate the shunt effects from inductor to the substrate node. The actual (circuit) connection is then made at schematic level using the 3-port data (or 4-port data if you have an additional port at inductor center tap).
edit: The single port for ground metal frame enables you to measure capacitance from inductor to that ground. However, that ground will not be included in the inductor current path, because port grounds are all at "global" ground.
If your goal is to also include current path through that ground path in results, you can indeed place one reference pin ("minus") for each inductor pin ("plus") instead of using global ground port reference at the bottom of the substrate. It really depends what you want/need to model, the "pure" inductor or some layout extract consisting of inductor and additional routing (here: current path in ground layer).