Are there any good database management applications for JDBC/Java databases? I am working with an Apache Derby/JavaDB database via JDBC. Before have I been working with MySQL and used phpMyAdmin as a good Database Management tool.

Is there any good desktop application for managing databases over JDBC?
DbVisualiser could fulfill your requirements as it supports quite a number of RDBMS, including JavaDB/Derby. You can see it in action below: 

The only question mark is if the free version has some limitations which are a stopper for you. You can check the matrix here.