Doing what I said seems to work to me

#!/usr/bin/perl --
use strict;
use warnings;
use WWW::Mechanize 1.73;

my $ua = WWW::Mechanize->new;

$ua->timeout(0.1);
$ua->add_handler("request_send",  sub { shift->dump; return });
$ua->add_handler("response_done", sub { shift->dump; return });
$ua->show_progress(1);

$ua->put_multi(
    'http://localhost',
    Content_Type => 'multipart/form-data',
    Content      => [
        fileuploadfieldname => [
            undef, # filename_to_read or none in this case
            "filenamesent",
            -content => 'i sent you some content named filenamesent'
        ],
    ],
);


sub WWW::Mechanize::put_multi {
    my( $self, $uri, @parameters ) = @_;

    $uri = $uri->url if ref($uri) eq 'WWW::Mechanize::Link';

    $uri = $self->base
            ? URI->new_abs( $uri, $self->base )
            : URI->new( $uri );
    
    unshift @parameters, $uri->as_string;
    
    require HTTP::Request::Common;
    
    my @suff = $self->_process_colonic_headers(\@parameters,1);
    my $req = HTTP::Request::Common::POST(
        @parameters,
    );
    $req->method('PUT');
    return $self->request( $req, @suff );
}

__END__


$ perl lwp-mechanize-put-multipart-form.pl
** PUT http://localhost ==> PUT http://localhost
Accept-Encoding: gzip
User-Agent: WWW-Mechanize/1.73
Content-Length: 163
Content-Type: multipart/form-data; boundary=xYzZY

--xYzZY\r
Content-Disposition: form-data; name="fileuploadfieldname"; filename="
+filenamesent"\r
-Content: i sent you some content named filenamesent\r
\r
\r
--xYzZY--\r\n
500 Can't connect to localhost:80
Content-Type: text/plain
Client-Date: Thu, 02 Apr 2015 08:49:31 GMT
Client-Warning: Internal response

Can't connect to localhost:80\n
No connection could be made because the target machine actively refuse
+d it. at .../site/lib/LWP/Protocol/http.pm line 49.\n
500 Can't connect to localhost:80 (1s)
Error PUTing http://localhost: Can't connect to localhost:80 at lwp-me
+chanize-put-multipart-form.pl line 62.
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