Saving a "craft-linkfield" field via an entry form
Found a solution by inspecting the HTML for the entry edit form in the CP. This works:

&lt;input id="fields-website-type" name="fields[website][type]" value="url" type="hidden"&gt;
&lt;input id="fields-website-isCpFormData" name="fields[website][isCpFormData]" value="true" type="hidden"&gt;
&lt;input id="website" type="text" name="fields[website][url]"&gt;