Programming is basically research and development You are building something which has never been built before. As such how do you estimate something if you have nothing to compare it to?
Actually though I have a limited amount of experience using Function Point Analysis. Some of the aspects of it are old, it was created before web apps became pervasive, but that doesn't matter. The principles are the same and there are dimensionless constants you can use to tune the FPA model to your organization. Eventually you end up with an empirical model of your programming team, development environment, tool suite, management efficiency, complexity of the problem domain, people quitting or dying, etc. You need to avoid over fitting however and recalibrate from time-to-time.
Agile keeps story points and velocity which serve the same purpose as the dimensionless constants of FPA. Unfortunately managers try to translate them to mythical man hours. But if you keep velocity or function points, whether you are using Agile or not, you should be able to get some idea. You have to be a bit scientific about it.
That and 'T-Shirt Sizing' is about as good as it gets.