If you are planning on testing yourself on something you have not been training or practicing you should hear the old Lost in Space line - "Danger Will Robinson - Danger...." - playing in your head. Especially if it is a 1 rm test.
Dropping and seeing where you are with push-ups (while not a perfect idea) carries far less risk then loading an un-practiced movement pattern with a maximal load. One wrong move and BLAMMO... There goes something wrong.
Unlike riding a bike there are a great many athletic movements that need to be trained and practiced before being tested. Squats being just one example (and a personal one). I had built a great base of strength through deadlifting and single leg squats and decided I would set a squat 1 rm (so I could run my percentages correctly). Well after hitting my first squat attempt I was told that I wasn't quite deep enough and to "go deeper" on the next attempt. So I added some weight and tried to go deeper - and BLAMMO...there went my disc. (As I said yesterday this was an old high school injury)
Lessons learned - #1 - Practice a lift before testing it. #2 - Sometimes a restricted range of motion is there for a reason and going beyond it may not be a good idea. #3 - Be happy with a PR and know that you do not have to shoot for a "max".
Practice a lift before testing it is self explanatory but let me explain further ;) You should be familiar witha movement pattern before testing it. Taking 2-4 weeks to "learn" a lift before testing is essential. This goes for strength/endurance tests like push-ups - No stress on an area > to maximal stress and fatigue on an area might not be the best way to treat yourself.
Sometimes a restricted range of motion is there for a reason. Your body builds in restrictions and asymmetries for any number of reasons (injury, posture etc...) and once they are there - they need to be dealt with before "pushing" through them. This is an example of the Jones Maxim - Just because you can doesn't mean you should. Screening and corrective strategies are there for a reason.
Be happy with a PR - you don't have to hit a "max". Sometimes you end up at a true maximum attempt - but as a general rule this should be reserved for meets and competition. If your previous best bench was 255 and you hit 275 - walk away with the PR - don't figure that "you had 295 in you" - cycle back work up again and by the time you "test" again you might just break that 300 barrier. Pushing for a max might be the straw that breaks the camel's shoulder.
These are lessons hard learned and recovered from.