Check samples from ArcGIS Runtime SDK for WPF under Geometry -> Geometry operations -> Project and Project Online
If that doesn't help, let us know.
WebMercator mercator = new WebMercator(); var mp = mercator.FromGeographic(new MapPoint(mapPoint.X, mapPoint.Y));
LocalGeometryService.GetServiceAsync(lgs => { _geometryTask = new GeometryService(); _geometryTask.Url = lgs.UrlGeometryService; _geometryTask.ProjectCompleted += geometryService_ProjectCompleted; _geometryTask.Failed += geometryService_Failed; });After this is completed, you should have access to the GeometryService through task (_geometryTask). You should get the UrlGeometryService from lgs parameter.See also http://resources.arcgis.com/en/help/runtime-wpf/concepts/index.html#//017000000039000000
What is your maps SpatialReference? If you don't set it explicitly it get SpatialReference from first layer (usually basemap).
If you can use LocalGeomteryService in your application you can use the code from Project example:LocalGeometryService.GetServiceAsync(lgs => { _geometryTask = new GeometryService(); _geometryTask.Url = lgs.UrlGeometryService; _geometryTask.ProjectCompleted += geometryService_ProjectCompleted; _geometryTask.Failed += geometryService_Failed; });After this is completed, you should have access to the GeometryService through task (_geometryTask). You should get the UrlGeometryService from lgs parameter.See also http://resources.arcgis.com/en/help/runtime-wpf/concepts/index.html#//017000000039000000