A GC or project manager with chops would already know how to do it. It takes a specific skillset to manage big projects, anticipate cost and potential problems.

the most accurate is by the "board measure"...also called stick estimating....you'll not get that figure with a 24 hour turnaround...

the most widely used is unit cost estimating.... compile the items...attach a cost... mark up with a profit....done...

Use the word " Allowance" a lot in your contracts. For example, I'm allowing $7000.00 for drilling a 400 foot deep well. If we need to drill 600 feet, then the price will increase by x. Allow for weather conditions, materials shortages, permit delays, change orders, etc, etc.

My first thought is: How can anything be accurate with uncertainty?

Barbara Todaro and Candice A. Donofrio have great responses for you. 

See what Candice A. Donofrio and Barbara Todaro have to say.

My contractors quote a range if uncertain what lies beneath unless something is torn out. So, basically a minimum if face value and a maximum if they run into larger, hidden issues.

Philip,

We agree with Candice A. Donofrio A

 Where is Barbara Todaro?   She may have the answer.

My husband, general contractor, does a hard bid based on cost plus a percentage for his fee. He also builds in a contingency which may or may not be used. However, in lieu of fast rising construction costs plus weather delays, his clients know that the price is not fixed and can adjust based on their selections, changes, and time to build.  The quote is accurate at the time provided, but the further the build gets away from that date, the more inaccurate it can become.  He has had to rebid jobs after clients delayed a year and a half working in their design, and of course the price went up.  Plus changes they make during construction causes delays and added cost (their changes almost never make the cost less to build the home).

Estimates of each component of the project which can get fairly accurate with experience.

Barbara Todaro and Jeff Pearl have great answers for you.

In my opinion, you have conflicting components within your question of determining an "accurate method".  This is not possible with "many variables" and "uncertain time to completion."   If I had to give an answer, I'd say EXPERIENCE. 

Beyond that, listen to Barbara Todaro and Candice A. Donofrio.  They know way more than I do about such things. 

Find a better contractor.

There is no fast was for an accurate estimate unless the variables are priced in advance.

Okay it looks like hands down Barbara Todaro and Candice A. Donofrio have the answers!

Got me hanging which is not a helpful answer. There has to be software out there right?

It is their job to anticipate the unknown and add in for it. There are many great software apps now. Those old school guys have it in their head like the back of their hand thoughwhat to add or deduct for

Candice A. Donofrio nailed this one!

I would just have money held out grow until it is completed and make sure it's a lot of money...

Materials and labor and overhead and a whole lot of profit and contingency.

To get considered the initial quote is often low and quick schedule. You double their price and twice the initial time is what you ended up paying.....

I have no clue. I don't understand what you mean by "accurate method."

You have many great answers here.

I looked at the questions asked before and this one has a lot of great answers.

great answers here!

Pros are good at getting the timing down

No idea.

The one they will honor...no matter what.

What I ask my contractors for an estimate, I get an accurate estiamte for anything I know I absolutely need, then get additional estimates for options I may be considering...

Getting as accurate an estimate as possible with detail so there are no problems with what is being asked of them to complete is essential to rehabs, etc. 

Not sure what you mean?  Accurate method to quote a project??  Quote the actual prices... if you're an experienced contractor, you know what things cost.

A lot of contingency estimates built in. Long and short, uncertain is the guess!

Philip Eide I like Jeff Pearl 's answer. You have to put everything in the contract.

All the GC can hope to do is be accountable for  he figures they publish with the associated disclaimers. The project quote could be substantially different based on resources from on GC to another. So accuracy is a bit foggy.

My suggestion is to create your 'app' on JoistApp and modify it to exploit your skills, resources, influence and experience.

If you don't control the resources, you CAN"T control the time.

Just make an honest quote with contingencies.

wish I knew

Philip Eide - excellent answer from Barbara Todaro. 

Experience.