.NET WebService Error Handling Design

I am faced with a design/architectural problem, and can't figure out a clean solution. We have a .NET WebService with hundreds of WebMethods. (See example below). If any of the called WebMethods throws an unhandled exception, we want to generate an email.

Question: What would be a clean design pattern to use in such a situation. I want to avoid inserting repetitive code into hundreds of methods?

[WebService(Namespace = "http://example.com/")]
[WebServiceBinding(ConformsTo = WsiProfiles.BasicProfile1_1)]
[Serializable]
public class WebService : System.Web.Services.WebService
{
    [WebMethod]
    public string GetQuoteInfo(string request)
    {
        return QuoteService.GetQuoteInfo(request);
    }

    [WebMethod]
    public string GetQuoteAPR(string request)
    {
        return QuoteService.GetQuoteAPR(request);
    }

    [WebMethod]
    public string GetAccountContactInfo(string request)
    {
        return AccountService.GetAccountContactInfo(request);
    }

    ...
    ...
    ...

    [WebMethod]
    public string GetAccountContactInfo(string request)
    {
        // implementation
    }

}