Example
ClientContext oClientContext = new ClientContext("http://MyServer/sites/MySiteCollection");
File oFile = oClientContext.Web.GetFileByServerRelativeUrl("Default.aspx");
LimitedWebPartManager limitedWebPartManager = oFile.GetLimitedWebPartManager(PersonalizationScope.Shared);
oClientContext.Load(limitedWebPartManager.WebParts,
wps => wps.Include(
wp => wp.WebPart.Title));
oClientContext.ExecuteQuery();
if (limitedWebPartManager.WebParts.Count == 0)
{
throw new Exception("No Web Parts on this page.");
}
WebPartDefinition oWebPartDefinition = limitedWebPartManager.WebParts[1];
WebPart oWebPart = oWebPartDefinition.WebPart;
oWebPart.Title = "My New Web Part Title";
oWebPartDefinition.SaveWebPartChanges();
oClientContext.ExecuteQuery();
