How can I filter/find on an ElementCriteriaModel?
Update
I may have found a better option for you. Looks like you were on the right track after all, but with some quotes misplaced.

{% set entries = craft.entries.section('mySection') %}
{% set entry = entries.find({myFieldHandle:'mySearchVariable'})[0] %}
{{ entry.title }}


Although looks like this hits the database again (thanks carlcs).

Maybe back to the orginal answer then, which was:

{% set entries = craft.entries.section('mySection') %}
{% for entry in entries if entry.myFieldHandle == 'myVariable' %}
    {{ entry.title }}
{% endfor %}