In an incomplete market, vanilla options are independent assets like stocks or bonds. So the best way of thinking about how they are priced is the same way equilibrium prices in those markets occur: If too many people try to buy an option at a given strike then they push the price of those options up and we see that as the implied volatility increasing. The real thing here is the price of the option increasing, the implied volatility is a quoting convention but secondary to the dollar price. The opposite happens if too many people try sell a given strike in the market.
The models required in equilibrium markets are different to those required in derived markets. In fact you do not need a model if the market is liquid enough. You could be doing technical analysis on charts and thinking implied volatility is historically low and supported by some future event and thus bid and offer accordingly. Once again think stocks, not black-scholes. Pretty much all vanilla markets work this way, from credit and bonds to fx and equities. Remember people were trading options way before the Black-Scholes-Merton papers.
You need a complex model if you want to derive some exotic options value from the base market where your world of hedging instruments include vanilla options and the underlying instruments. The model gives you a arbitrage free way of interpolating the prices of your base instruments and vanilla options and thus arriving at your exotic options value. That is the reason you calibrate this models - they are fancy interpolators and require base information to interpolate from.
Now if you find yourself in a market where vanilla options do not trade, then pick the simplest model you can intuit to map your intuition to option prices and behave accordingly. There is a reason black-scholes is everywhere! If you must price an exotic in that environment then an uncertain volatility model is not a bad first stab as the parameters once again allow you to interpolate from what you know (perhaps some historical upper and lower realized volatility bounds) into option prices.