I see this is a very old question but I was trying to do the same thing which brought me here. I'll add some info and my progress to date:
Firstly, the reason you get an estimate that can change wildly is because search engines use probabilistic algorithms to calculate relevance. This means that during a query they do not need to examine all possible matches in order to calculate the top N hits by relevance with a fair degree of confidence. That means that when the search concludes, for a large result set, the search engine actually doesn't know the total number of hits. It has seen a representative sample though, and it can use some statistics about the terms used in your query to set an upper limit on the possible number of hits. That's why you only get an estimate for large result sets. Running the query in such a way that you got an exact count would be much more computationally intensive.
The best I've been able to achieve is to refine the estimate by tricking the search engine into looking at more results. To do this you need to go to page 2 of the results and then modify the 'first' parameter in the URL to go way higher. Doing this may allow you to find the end of the result set (this worked for me last year I'm sure although today it only worked up to the first few thousand). Even if it doesn't allow you to get to the end of the result set you will see that the estimate gets better as the query engine considers more hits.
I found Bing slightly easier to use in the above way - but I was still unable to get an exact count for the site I was considering. Google seems to be actively preventing this use of their engine which isn't that surprising. Bing also seems to hit limits although they looked more like defects.
For my use case I was able to get both search engines to fairly similar estimates (148k for Bing, 149k for Google) using the above technique. The highest hit count I was able to get from Google was 323 whereas Bing went up to 700 - both wildly inaccurate but not surprising since this is not their intended use of the product.
If you want to do it for your own site you can use the search engine's webmaster tools to view indexed page count. For other sites I think you'd need to use the search engine API (at some cost).