How do I store my client's passwords securely and make them retrievable?
Try either the Field Encrypt module:


  Adds options to encrypt field values.
  
  The goal of this module is to create a method for encrypting field
  values when stored in the database.
  
  This module depends on the Encrypt module
  (http://drupal.org/project/encrypt) for encrypting and decrypting
  strings.


Or which sounds better for your use-case of "settings" the Encrypted Settings Field module:


  This module adds the "encrypted settings" field through Field API,
  which has the following two features:
  
  
  The field can be encrypted before saving to the database
  The field can be validated to follow INI format
  
  
  This module is ideal to save
  credential settings information, such as a "Credit Card" field to add
  to users' profile.


A more developer friendly form which stores the final encrypted value into the drupal database and plays nicely with Drupal 7 core Form API elements is the Encrypt Form API module:


  After installing and enabling this module, you will be able to add an
  '#encrypt' property to any of the following supported Form API element
  types:
  
  
  textfield
  textarea
  checkboxes
  checkbox
  radios
  radio
  select
  password
  password_confirm
  


To use this module I would recommend assuring your site is served only in SSL, then the contents of the field is encrypted on save, after normal form validation occurs.