I have read that when you have a high proportion of infected cells in the lowest dilution the spreaman-karber method is quite useful but not when the TCID50/mL is zero. we need a solution for this in the lab for viral validation.
You could try immunestaining assays. If you are working with virus produces no cytopathic effect. Fix your infected cells 24-48 hours post infection, permealize cells and stain your infected cells with primary antibody( specific antibody against your virus) conjugated with HRP for example, and finally add the specific substrate for HRP and check under the microscope.
I would have done qPCR which linearly amplify the a. Virus specific fragment and b. cell specific fragment. In that way you can normalize the virus titre using the total number of cells. Hope it works as I didn't do this before.
Laura Carballo Sigler you may want to try VN- titres, Haemagglutination assays (direct or indirect) or specific ELISA for viral titre detection depending upon the nature and surface antigens of your virus.