Here is an answer based on that by Anubis (which is a better approach as it doesn't modify the headers for every request) but which is more equivalent to the code in the original question:
using Newtonsoft.Json;
...
var client = new HttpClient();
var httpRequestMessage = new HttpRequestMessage
{
Method = HttpMethod.Post,
RequestUri = new Uri("https://api.clickatell.com/rest/message"),
Headers = {
{ HttpRequestHeader.Authorization.ToString(), "Bearer xxxxxxxxxxxxxxxxxxx" },
{ HttpRequestHeader.Accept.ToString(), "application/json" },
{ "X-Version", "1" }
},
Content = new StringContent(JsonConvert.SerializeObject(svm))
};
var response = client.SendAsync(httpRequestMessage).Result;