use UTF8选项

request.DefaultRequestHeaders.Authorization = 
new AuthenticationHeaderValue(
    "Basic", Convert.ToBase64String(
        System.Text.Encoding.UTF8.GetBytes(
           $"{yourusername}:{yourpwd}")));

在net .core中，您可以使用Identity Server 4

var client = new HttpClient();
client.SetBasicAuthentication(userName, password);

or

var client = new HttpClient();
client.SetBearerToken(token);

参见https://github.com/IdentityModel/IdentityModel/blob/main/src/Client/Extensions/AuthorizationHeaderExtensions.cs

方法是这样的，

httpClient.DefaultRequestHeaders.Authorization =
    new AuthenticationHeaderValue("Bearer", "Your Oauth token");

使用现有的库可能更容易。

例如，Identity Server 4中添加了下面的扩展方法 https://www.nuget.org/packages/IdentityModel/

 public static void SetBasicAuthentication(this HttpClient client, string userName, string password);
    //
    // Summary:
    //     Sets a basic authentication header.
    //
    // Parameters:
    //   request:
    //     The HTTP request message.
    //
    //   userName:
    //     Name of the user.
    //
    //   password:
    //     The password.
    public static void SetBasicAuthentication(this HttpRequestMessage request, string userName, string password);
    //
    // Summary:
    //     Sets a basic authentication header for RFC6749 client authentication.
    //
    // Parameters:
    //   client:
    //     The client.
    //
    //   userName:
    //     Name of the user.
    //
    //   password:
    //     The password.
    public static void SetBasicAuthenticationOAuth(this HttpClient client, string userName, string password);
    //
    // Summary:
    //     Sets a basic authentication header for RFC6749 client authentication.
    //
    // Parameters:
    //   request:
    //     The HTTP request message.
    //
    //   userName:
    //     Name of the user.
    //
    //   password:
    //     The password.
    public static void SetBasicAuthenticationOAuth(this HttpRequestMessage request, string userName, string password);
    //
    // Summary:
    //     Sets an authorization header with a bearer token.
    //
    // Parameters:
    //   client:
    //     The client.
    //
    //   token:
    //     The token.
    public static void SetBearerToken(this HttpClient client, string token);
    //
    // Summary:
    //     Sets an authorization header with a bearer token.
    //
    // Parameters:
    //   request:
    //     The HTTP request message.
    //
    //   token:
    //     The token.
    public static void SetBearerToken(this HttpRequestMessage request, string token);
    //
    // Summary:
    //     Sets an authorization header with a given scheme and value.
    //
    // Parameters:
    //   client:
    //     The client.
    //
    //   scheme:
    //     The scheme.
    //
    //   token:
    //     The token.
    public static void SetToken(this HttpClient client, string scheme, string token);
    //
    // Summary:
    //     Sets an authorization header with a given scheme and value.
    //
    // Parameters:
    //   request:
    //     The HTTP request message.
    //
    //   scheme:
    //     The scheme.
    //
    //   token:
    //     The token.
    public static void SetToken(this HttpRequestMessage request, string scheme, string token);

BaseWebApi.cs

public abstract class BaseWebApi
{
    //Inject HttpClient from Ninject
    private readonly HttpClient _httpClient;
    public BaseWebApi(HttpClient httpclient)
    {
        _httpClient = httpClient;
    }

    public async Task<TOut> PostAsync<TOut>(string method, object param, Dictionary<string, string> headers, HttpMethod httpMethod)
    {
        //Set url

        HttpResponseMessage response;
        using (var request = new HttpRequestMessage(httpMethod, url))
        {
            AddBody(param, request);
            AddHeaders(request, headers);
            response = await _httpClient.SendAsync(request, cancellationToken);
        }

        if(response.IsSuccessStatusCode)
        {
             return await response.Content.ReadAsAsync<TOut>();
        }
        //Exception handling
    }

    private void AddHeaders(HttpRequestMessage request, Dictionary<string, string> headers)
    {
        request.Headers.Accept.Clear();
        request.Headers.Accept.Add(new MediaTypeWithQualityHeaderValue("application/json"));

        if (headers == null) return;

        foreach (var header in headers)
        {
            request.Headers.Add(header.Key, header.Value);
        }
    }

    private static void AddBody(object param, HttpRequestMessage request)
    {
        if (param != null)
        {
            var content = JsonConvert.SerializeObject(param);
            request.Content = new StringContent(content);
            request.Content.Headers.ContentType = new MediaTypeHeaderValue("application/json");
        }
    }

SubWebApi.cs

public sealed class SubWebApi : BaseWebApi
{
    public SubWebApi(HttpClient httpClient) : base(httpClient) {}

    public async Task<StuffResponse> GetStuffAsync(int cvr)
    {
        var method = "get/stuff";
        var request = new StuffRequest 
        {
            query = "GiveMeStuff"
        }
        return await PostAsync<StuffResponse>(method, request, GetHeaders(), HttpMethod.Post);
    }
    private Dictionary<string, string> GetHeaders()
    {
        var headers = new Dictionary<string, string>();
        var basicAuth = GetBasicAuth();
        headers.Add("Authorization", basicAuth);
        return headers;
    }

    private string GetBasicAuth()
    {
        var byteArray = Encoding.ASCII.GetBytes($"{SystemSettings.Username}:{SystemSettings.Password}");
        var authString = Convert.ToBase64String(byteArray);
        return $"Basic {authString}";
    }
}

6年过去了，但为了帮助别人，我加了这个。

https://www.codeproject.com/Tips/996401/Authenticate-WebAPIs-with-Basic-and-Windows-Authen

var authenticationBytes = Encoding.ASCII.GetBytes("<username>:<password>");
using (HttpClient confClient = new HttpClient())
{
  confClient.DefaultRequestHeaders.Authorization = new AuthenticationHeaderValue("Basic", 
         Convert.ToBase64String(authenticationBytes));
  confClient.DefaultRequestHeaders.Accept.Add(new MediaTypeWithQualityHeaderValue(Constants.MediaType));  
  HttpResponseMessage message = confClient.GetAsync("<service URI>").Result;
  if (message.IsSuccessStatusCode)
  {
    var inter = message.Content.ReadAsStringAsync();
    List<string> result = JsonConvert.DeserializeObject<List<string>>(inter.Result);
  }
}