Currently in models.py I have 
class ModelName(models.Model):
    rowname = models.CharField(max_length=100, blank = True, unique=True) 
This does wonders as far as making sure the same value isn't submitted to the database twice but is there a way that I can have unique not raise an error when the value that is a duplicate is an empty string? Does unique take an exception argument?
Essentially, you need to follow the advice in this answer. While Django considers '' equal to '' for purposes of uniqueness, it doesn't consider NULL equal to NULL. So you need to store NULL values instead of empty strings.
Change the field to allow NULL, by adding null = True in your model:
rowname = models.CharField(..., blank = True, null = True, unique = True) 
Change empty strings to None in the form:
class ModelNameForm(forms.ModelForm):
    class Meta:
        model = ModelName
    def clean_rowname(self):
        return self.cleaned_data['rowname'] or None
class ModelNameAdmin(admin.ModelAdmin):
    form = ModelNameForm
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