Until MAMP releases a new version for Maverick, there is a trick to make it work:
You just need to open keychain access, click on it’s menu bar item “Keychain Access”, then “Certificate Assistant”, and “Create a Certificate”. For Name, enter your name, Identify Type should be kept as Self Signed Root, and Certificate Type should be code signing. You can pretty much click continue on everything else until your certificate.
Finally, open terminal, and run:
codesign -s “Your Name” /Applications/MAMP\ Pro/MAMP\ Pro.app
This tip is taken from here: