It seems when you use the 'Create a new self-signed certificate...' option for a host, Apache cannot start, and throw this error in the apache_error.log:
You can manually generate the Certificate file (.crt), and Certificate key file (.key):
openssl genrsa 2048 > host.key
chmod 400 host.key
openssl req -new -x509 -nodes -sha256 -days 365 -key host.key -out host.cert
Choose the new files, and restart MAMP.
Optionally, you can inspect the Certificate file:
openssl x509 -in certificate.crt -text -noout