Is there such a thing as a wildcard character in Java?

You can use regular expressions:

if (em1.matches("524[0-9]{2}646")) {
  // do stuff
}

For Java specific documentation see the Pattern class. For some uses of regular expressions (such as in the sample above), there are shortcut methods in String: matches(), replaceAll()/replaceFirst() and split().

regular-expressions.info has good documentation on regular expression in general.

You can solve it easily using regular expressions:

if (em1.matches("524..646"))

for instance.

(The . is a wildcard that stands for any character. You could replace it with \\d if you like to restrict the wildcard to digits.)

Here is a more general variant that matches "0" against any character:

String em1 = "52494646";
String em2 = "52400646";

if (em1.matches(em2.replaceAll("0", "\\\\d"))){
    System.out.println("Matches");
}

Usually you can do a combination of startsWith, endsWith, or contains to find if a String start with, ends with or contains another string. You can uses these in combination like

number.startsWith("524") && number.endsWith("646");

Using a regular expression is likely to be a better choice 95% of the time but is more expensive.