In case anyone was curious, I was able to figure this out based on all of your responses combined!
This is in the Facelet:
<h:form id="myform">
<h:inputSecret value="#{createNewPassword.newPassword1}" id="newPassword1" />
<h:message class="error" for="newPassword1" id="newPassword1Error" />
<h:inputSecret value="#{createNewPassword.newPassword2}" id="newPassword2" />
<h:message class="error" for="newPassword2" id="newPassword2Error" />
<h:commandButton value="Continue" action="#{createNewPassword.continueButton}" />
</h:form>
This is in the continueButton() method:
FacesContext.getCurrentInstance().addMessage("myForm:newPassword1", new FacesMessage(PASSWORDS_DONT_MATCH, PASSWORDS_DONT_MATCH));
And it works! Thanks for the help!