How to access students who miss test or quizzes during the semester

As a part-time university lecturer, every semester I have students who miss a test or a quiz during a course. If they get a certificate of absence from the university then it is not problem – the other assessments are simply given more weight.

However, sometimes a student may catch a cold or may have some other circumstance (last year, a student couldn't make the test because they noticed a stray dog and had to wait for the police to come to collect it!) which is not worthy enough of a certificate of absence. Or a student may just miss a test because they deemed something else to be more important. Whatever the case, I don't think I should simply reweight the other assessments – their should be some consequence for them missing a test. But at the same time I don't want them to score a zero and lose a large percentage of their grade (many of my assessments are worth 20%).

Is there a middle ground? Recently, I have reweighted the other assessments but deducted points from the final grade. Example: Say I have 2 reports (10% each) and 4 unit tests (20% each). Let's say the student misses a test but gets 15/20 for the reports and 45/60 for the other three tests (60/80). If a student misses a test without a certificate of absence, then there are three options:

A: They simply get a zero for the missed test. In which case their grade about be 60/100. A bit harsh?

B: The weights are adjusted for the other assessments that they did complete: Reports become 18.75/25 and the tests become 56.25/75 (an increase of 25%). That gives them a grade of 75/100. Too lenient?

C: My method is to adjust the weight of the other assessments, as in B above, but to deduct 10 points from the final grade (10 points is half of the 20% that the missed assessment was worth). That leaves them with 65/100.

I think C is a good middle-ground but it is hard to explain to students in the syllabus. So I wanted to ask what other teachers do in situations where a student misses an assessment.

Note: If a student misses a report, they get zero. My reasoning is that they have a week to finish a report whereas a test is a one-off event.

EDIT: I don't want to do make-up tests because as a part-timer with 17 classes a week I simply do not have time and I find that a lot of the time it ends up in a back and forth negotiation with the student as to when they can do the test.