upgrading inductor

What do you mean by "higher gauge"? If you intend to use thinner wire (skin effect) and keep the same resistance and inductance you can achieve this by using tape woven inductors. Many good speakers have tape inductors but also many very good speakers don't. I doubt if it makes any difference because skin effect in copper at 20kHz starts at gauge 18 but at this frequency but overall effect is negligible.

Kij,
The OP has left the building.

I've had success upgrading capacitors, but I never tried inductors. Can anyone relate the audible difference of this upgrade?

It's all about tradeoffs and the original inductor.

If the original inductor is aircore, and larger gauge wire, don't bother.

IF the original inductor is iron core 16 or 18 ga in a fairly low sensitivity speaker, like my Magnepans, than you can get some headroom out of going to larger gauge wire as long as you consider the DCR of the new piece. Changing the DCR will alter the crossover point...but usually not much AND change driver balance and perhaps voicing. 1db would be a large change in my panels.

Inductors in mids and tweets? much less important than in the bass where most of the power goes. That is the best use of a new inductor...in the bass. And than only if you are a 'power user' and routinely crank it up.

Inductor calculators? yep...and plenty on line. Run some 'simulations' My design for my panels new inductor? 14ga......up from 16, aircore and with a DCR within 5% of the original unit. It is also the same number of layers as winds, so the coil is square in cross section AND I designed it to be wound on a standard size of PVC pipe, right from the home store. Outside diameter is a tick over 4" and less than 1" thick, so it is a manageable size.