Dang, I didn't read the documentation enough! The section on Clash Detective had a good example of what to do:
DocumentClash document_clash =
Autodesk.Navisworks.Api.Application.MainDocument.GetClash();
// get an existing test
ClashTest test = document_clash.TestsData.Tests[test_index] as ClashTest;
// test read from document-part is read-only, create a copy
ClashTest new_test = test.CreateCopy() as ClashTest;
// edit the properties, results and result-groups of the new_test
// Now replace the test stored in the document with the whole of
// our edited hierarchy. This is efficient as a way of doing many
// edits in one operation.
document_clash.TestsData.TestsReplaceWithCopy(test_index, new_test);