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I have several estimates obtained using different softwares, these programs give me an estimate as well as a 95% confidence interval. However, these CIs are not symmetric around my point estimates, the upper confidence interval is generally much larger. I want to weight these estimates by their uncertainty, but I am not sure how to do this when dealing with asymmetric CIs.

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More information is necessary. What are the parameters being estimated? What procedure are you using? – Macro Oct 6 '11 at 13:42
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Have you checked them on all scales? For example, if you take the natural log of your estimate and the confidence intervals, are they symmetric? – EpiGrad Oct 6 '11 at 18:10

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