C#

using DotNetBrowser;
using DotNetBrowser.DOM;
using DotNetBrowser.Events;

...

Browser browser = BrowserFactory.Create();
browser.FinishLoadingFrameEvent += delegate(object sender, FinishLoadingEventArgs e)
{
    if (e.IsMainFrame)
    {
        DOMDocument document = e.Browser.GetDocument();
        DOMSelectElement select = (DOMSelectElement) document.GetElementById("select-tag");
        SelectOptionByIndex(select, 2);
    }
};
browser.LoadHTML("<html><body><select id='select-tag'>\n" +
        "  <option value=\"volvo\">Volvo</option>\n" +
        "  <option value=\"saab\">Saab</option>\n" +
        "  <option value=\"opel\">Opel</option>\n" +
        "  <option value=\"audi\">Audi</option>\n" +
        "</select></body></html>");

...

private static void SelectOptionByIndex(DOMSelectElement selectElement, int index)
{
    List<DOMOptionElement> options = selectElement.Options;
    DOMOptionElement option = options[index];
    option.Selected = true;
}

VB.NET

Imports DotNetBrowser
Imports DotNetBrowser.DOM
Imports DotNetBrowser.Events

'...

Dim browser As Browser = BrowserFactory.Create()
AddHandler browser.FinishLoadingFrameEvent, sub(ByVal sender As Object, ByVal e As FinishLoadingEventArgs)

    If e.IsMainFrame Then
        Dim document As DOMDocument = e.Browser.GetDocument()
        Dim [select] As DOMSelectElement = CType(document.GetElementById("select-tag"), DOMSelectElement)
        SelectOptionByIndex([select], 2)
    End If
End sub

browser.LoadHTML("<html><body><select id='select-tag'>" & vbLf & "  <option value=""volvo"">Volvo</option>" & vbLf &
                 "  <option value=""saab"">Saab</option>" & vbLf & "  <option value=""opel"">Opel</option>" & vbLf &
                 "  <option value=""audi"">Audi</option>" & vbLf & "</select></body></html>")

'...

Private Shared Sub SelectOptionByIndex(ByVal selectElement As DOMSelectElement, ByVal index As Integer)
    Dim options As List(Of DOMOptionElement) = selectElement.Options
    Dim [option] As DOMOptionElement = options(index)
    [option].Selected = True
End Sub