It should be possible to suppress serial warnings that are specific to a particular declaration such as a method or field.
Suppressing warnings for the whole class will obscure multiple warnings.

One specific example is:

% javac -Xlint A.java

A.java:10: warning: [serial] serialVersionUID must be of type long in class B
    private static final byte serialVersionUID = 5;
                              ^
1 warning
%

This warning can only be suppressed at the class level and adding suppress warning("serial") on the field is ignored.

A.java:

import java.io.Serializable;

@SuppressWarnings("serial") // Testing incorrect type of serialVersionUID
class A implements Serializable {
    private static final byte serialVersionUID = 5;
}

class B implements Serializable {
    @SuppressWarnings("serial") // Testing incorrect type of serialVersionUID
    private static final byte serialVersionUID = 5;
}


---
% java -version
java version "9"
Java(TM) SE Runtime Environment (build 9+181)
Java HotSpot(TM) 64-Bit Server VM (build 9+181, mixed mode)