I implemented my own HttpException and supporting middleware which catches all HttpException‘s and turns them into the corresponding error response. A short extract can be seen below. You can also use the Boxed.AspNetCore Nuget package.

Usage Example in Startup.cs

public void Configure(IApplicationBuilder application)
{
    application.UseIISPlatformHandler();

    application.UseStatusCodePagesWithReExecute("/error/{0}");
    application.UseHttpException();

    application.UseMvc();
}

Extension Method

public static class ApplicationBuilderExtensions
{
    public static IApplicationBuilder UseHttpException(this IApplicationBuilder application)
    {
        return application.UseMiddleware<HttpExceptionMiddleware>();
    }
}

Middleware

internal class HttpExceptionMiddleware
{
    private readonly RequestDelegate next;

    public HttpExceptionMiddleware(RequestDelegate next)
    {
        this.next = next;
    }

    public async Task Invoke(HttpContext context)
    {
        try
        {
            await this.next.Invoke(context);
        }
        catch (HttpException httpException)
        {
            context.Response.StatusCode = httpException.StatusCode;
            var responseFeature = context.Features.Get<IHttpResponseFeature>();
            responseFeature.ReasonPhrase = httpException.Message;
        }
    }
}

HttpException

public class HttpException : Exception
{
    private readonly int httpStatusCode;

    public HttpException(int httpStatusCode)
    {
        this.httpStatusCode = httpStatusCode;
    }

    public HttpException(HttpStatusCode httpStatusCode)
    {
        this.httpStatusCode = (int)httpStatusCode;
    }

    public HttpException(int httpStatusCode, string message) : base(message)
    {
        this.httpStatusCode = httpStatusCode;
    }

    public HttpException(HttpStatusCode httpStatusCode, string message) : base(message)
    {
        this.httpStatusCode = (int)httpStatusCode;
    }

    public HttpException(int httpStatusCode, string message, Exception inner) : base(message, inner)
    {
        this.httpStatusCode = httpStatusCode;
    }

    public HttpException(HttpStatusCode httpStatusCode, string message, Exception inner) : base(message, inner)
    {
        this.httpStatusCode = (int)httpStatusCode;
    }

    public int StatusCode { get { return this.httpStatusCode; } }
}

In the long term, I would advise against using exceptions for returning errors. Exceptions are slower than just returning an error from a method.