I am not an expert but--have a few things to ponder
The port size depends on the cross section area and using a screen limits the cross section so will change the tuning lower AND restrict the port flow causing chuffing and port compression. Both of those are not a good thing but I do have a few ponderings to limit that problem. I am not an expert, this is not approved by the FDA, my jibber-jabber has been known to cause cancer in California and your subwoofer might appear larger in a rear view mirror--you have been warned.
That being said, I would make a "screen box" or use the largest screen openings you can use and make a large "box" around the port(s) to get maximum screen area so to allow maximum air flow to be able to get to the poorts. For example, if you run two 3" ports which would be 3cR2X2 or 3 x 1.5x1.5 x 2 or 13.5 square inches--I'd go with a screen below the woofer but above the ports as a "box" of at least five times the surface area or larger to limit the disruption of flow. DON'T just slap a screen over the port as that reduces surface area of the port changing the tuning frequency etc.
The other option is to use passive radiators, they are a "mechanical port" or work basically like a tuning fork in operation but cost big bucks to do that. My subwoofers I built for my garage were designed to run ported in the summer and when the cold weather hits, I install plugs in the port to prevent small furry woodland creatures from setting up a winter home. Sealed in the winter and ported in the ummer works well.
The last option is to use a grill using acoustic cloth over the entire face of the subwoofer--try to keep the cloth at least an inch or two in front of the ports (or more) This might restrict the port a bit so use a very open mesh cloth if you can.
Good luck in your quest and always check the tuning of the box after you build either a screen box internal or external to ensure the proper operation of the port.