Broadly speaking, as you probably already know, there are 2 approaches to estimating large covariance matrices:
1) Shrinkage Methods like Ledoit-Wolf that try to reduce the noise in a large matrix (N by N) that has been estimated using the conventional method.
2) Factor Models of Covariance as described in for example Connor Korajczik 2007 that assume that only a small number of factors matter. This is pretty much what you have in mind when you mention "some sort of a PCA approach". A decent paper on estimating such models is Extracting factors from heteroskedastic asset returns, by Christopher S. Jones
On the practical side there is a big project at Blackrock directed by Andrew Ang that is developing and updating a huge factor-based risk model for a large number of markets that is the biggest covariance estimation that I know of. Bloomberg is also developing a large risk model of this kind.
There are a lot of practical issues that you have to deal with if you do the estimation yourself. One is that not all assets have been in existence for the same length of time (Stambaugh wrote about this in 'Analyzing Investments Whose Histories Differ in Length' in 1997). Another is that daily correlations between stocks trading on different exchanges are tricky because, for example the trading hours for New York and Tokyo are quite different. Also, because of these and other problems the covariance matrix you estimate often turns out to be non-positive definite, which causes problems when you run an optimizer. You have to check the matrix before you use it and fix it to be positive definite if necessary.