Is it possible to search a listview and restrict the items in the listview by the search criteria?

 private void displayDeliveries()
    {
        lstDeliveryDetails.Items.Clear(); 
        foreach (Delivery d in mainForm.myDeliveries)
        {
            ListViewItem item = lstDeliveryDetails.Items.Add(d.DeliveryName); 
            item.SubItems.Add(d.DeliveryAddress);
            item.SubItems.Add(d.DeliveryDay);
            item.SubItems.Add(d.DeliveryTime);
            item.SubItems.Add(d.DeliveryMeal);
            item.SubItems.Add(d.DeliveryInstructions);
            item.SubItems.Add(d.DeliveryStatus);
        }
    }

At the moment that code populates the listview.

private void btnSearch_Click(object sender, EventArgs e)
    {
        //reset the selection and get the searched text
        iDeliverySelected = -1;
        string searchValue = txtSearchBox.Text;

        //loop through to find the search
        for (int i = 0; i < myDeliveries.Count; i++)
        {
            Delivery d = (Delivery)mainForm.myDeliveries[i];

            if (d.DeliveryName == searchValue)
                MessageBox.Show("name matched");
        }


    }

So far this is what I have for search, I'm struggling to take it to the next level!

Could anyone offer an ideas? Thanks