So, my bag leaks

Hand driers are your friend for water  based wardrobe emergencies.

Splash water on the dry areas, no one will notice then.

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Get a dry bag from a camping shop and leave it in the pannier, if it's looking rainy put the essentials inside

No trouser presentation?
No wet patch to be seen.

Actually wet yourself during the presentation. Then you won't need to worry about them thinking you might have wet yourself.

It's a great story to start your presentation with and will ensure you capture everyone's attention.

Channel your inner Clark Kent and wear your undies on the outside

Go commando/Donald Duck as necessary.

Always keep spare underwear at work.

I once had to do a presentation to the director of education and about 100 other headteachers etc. Rode there, snapped my chain, fixed it, cleaned hands when I got there and did the presentation. Afterwards I looked in the mirror and I looked like I had escaped from a strangling, oily marks around my neck when I put my helmet back on

Full set of clothes at work for this very reason!

Well mine leaked onto a folded shirt, so it looked like I had leaky nipples at the start of the day. Luckily it wasn't one of my big morning meeting days.

I thought Ortlieb panniers were worth the money, but apparently not.

I once had a salad containing beetroot in the same rack bag as my shirt for the day. Turns out the tupperware wasn't very watertight. Lots of pink spots all over the body of the shirt. Spent the whole day wearing a hi-vis over the top to cover the worst of it. Lessons were learnt.