Building a string from multiple inputs with some variations
String.Format("{0}{1}{2}{3}{4}{5}{6}", ...);


Since you are just doing concatenation, string.Concat is more appropriate here.

if (!String.IsNullOrEmpty(model.Seed.GID) &amp;&amp; !String.IsNullOrEmpty(model.Seed.Clone))
{
    SeedRefId = String.Format("{0}{1}{2}{3}{4}{5}{6}{7}{8}",
    model.Customer.CustomerCode.TrimEnd(), model.Seed.CollectionCodeId.TrimEnd(), model.Seed.SpeciesId.TrimEnd(),
    model.Seed.Zone.TrimEnd(), model.Seed.Elevation.TrimEnd(), model.Seed.ColYear.TrimEnd(), model.Seed.OrchardId, model.Seed.GID.TrimEnd(), model.Seed.Clone.TrimEnd());
    return SeedRefId;
} 


Between your ifs and else, there is a lot of repeated code. And, we can observe a pattern there:


The first 7 elements are always present.
The last 2 elements are present if it is not null/empty
The elements are always in the same order.




The method can be reduced to this:

private string ConstructSeedReference(SeedViewModel model)
{
    var reference = string.Concat(
        model.Customer.CustomerCode.TrimEnd(), 
        model.Seed.CollectionCodeId.TrimEnd(), 
        model.Seed.SpeciesId.TrimEnd(),
        model.Seed.Zone.TrimEnd(), 
        model.Seed.Elevation.TrimEnd(), 
        model.Seed.ColYear.TrimEnd(), 
        model.Seed.OrchardId);

    if (!string.IsNullOrEmpty(model.Seed.GID))
    {
        reference += model.Seed.GID.TrimEnd();
    }

    if (!string.IsNullOrEmpty(model.Seed.Clone))
    {
        reference += model.Seed.Clone.TrimEnd();
    }

    return reference;
}




EDIT: Just reread your question, if your concern is only about the NullReferenceException. You can simply use null-coalescing operator ?.:

private string ConstructSeedReference(SeedViewModel model)
{
    return string.Concat(
        model.Customer.CustomerCode.TrimEnd(),
        model.Seed.CollectionCodeId.TrimEnd(),
        model.Seed.SpeciesId.TrimEnd(),
        model.Seed.Zone.TrimEnd(),
        model.Seed.Elevation.TrimEnd(),
        model.Seed.ColYear.TrimEnd(),
        model.Seed.OrchardId,
        model.Seed.GID?.TrimEnd(),
        model.Seed.Clone?.TrimEnd());
}