I've made iPhone Mounts for both telescopes and microscopes in the past. Each of these required me to remove my case first before I could use them. I decided to try to make a mount that wouldn't require this. It was also important to me to make one mount that I could use on either a telescope or a microscope.
I don't know how universal this mount actually is, but I do know it will fit an iPhone 5 or 6 either with or without a case. There's a lot of room for adjustment, so I'm sure it will also work with many other phones as well. It also fits our school's compound and dissecting microscopes as well as out telescopes.
When using this it is important to keep some distance between the phone camera and the scope eyepiece. The only way to avoid vignetting is to use the digital zoom on your phone. For optimal field of view make sure your vignetting circle has crisp edges.
The screws on the phone holder portion were printed with 6 perimeters for strength. I could have just used a high infill. However I didn't need the knobs to be solid. With 6 perimeters the screw part is pretty solid.
Everything else was printed at 10% infill with only 3 perimeters. Only the "Clamp Clip" requires any support.
The screws on the phone mount were made in OpenSCAD using Nut_Job by mike_matta. I took the long screw into Tinkercad to make the smooth shaft portion wider. Some of the scope mount came from G-Clamp by johann517. One of these days I will learn how to make my own threaded parts, but until then I'm sure I will continue to rely on both of these.
All the rest was designed in Autodesk Fusion360. This was the first project I've made in this program, so there was a lot of learning going on.
This was printed with PETG. The phone holder bends a little when tightened. Printing in PLA might help mitigate this, but I haven't tried that to know for sure. This is actually my fifth version of the phone holder. The bend is small enough now that it doesn't overly annoy me, so I think I'm done.