Economic capital (EC) is a risk measure that has been used by financial firms to help determine capital levels to hold to protect (with high probability) against large unexpected losses of credit portfolios. Given a stochastic model for a portfolio's loss over a given time horizon, the EC is defined as the difference between a quantile and the mean of the loss distribution. We describe Monte Carlo methods for estimating the EC. We apply measure-specific importance sampling to separately estimate the two components of the EC, which can lead to much smaller variance than when estimating both terms simultaneously. We provide Bahadur-type representations for our estimators of the EC, which we further exploit to establish central limit theorems and asymptotically valid confidence intervals. We present numerical results for a simple model to demonstrate the effectiveness of our approaches.