I was just digging around for info on estimating and was drilling into COCOMOII which is a model used for estimating effort developed by Barry Boehm. It's worth thr trip over to Wikipedia to at least get the basics.
The headline I'll share here is that the essence of the estimation process covers a number of factors which include the following.
Have you done this before? The degree of precedence within your orgasnation for simialr work will affect your ability to both estimate and to actually deliver the right solution.
How flexible are your goals and processes? If this project is THE project that is going to develop a whole bunch of architectural foundation work you are going to cost more than others. If you are stuck with a heavy and bureacratic process - you are stuck with it and the accompanyting work and cost.
How scalable and robust does your soluton need to be? Quality = cost. Look for the payoff curve.
How well does your team work together? Are there boundary disputes? Doe poeple like working together? This stuff matters a lot.
Does this sound sensible to you?
There are other methods and there is the no method method. Whatever models you use, make sure you have informed yoruself about the options.