Oh, absolutely.

In fact, when one of my carpenters f.cks himself up so badly that he's
on bedrest, that's the kind of job I have them do to stay sharp.

If all you are interested in doing is listening, a simple scanner would
do that and you do not need to worry about licensing.

Most of your modern handheld transcievers have very good receivers in
them so there really isn't much you are going to be able to do to the
unit itself to increase your range.

A simple outside antenna will work wonders and increase your receive
range tremendously.  I am assuming your handheld unit has one of the
"rubber duck" flexible antennas.  These are at best, a poor compromise
that sacrifice performance for size.

Depending on how the antenna is connected to the radio will determine
how hard it is to connect an outside antenna.  Some radios have a BNC
connector on the top which makes it very easy to remove the portable
antenna and connect an outside antenna.  You mention impedance matching,
which makes me think you have some electronic background so you probably
know something of the antenna connection.

This will bring me to the outside antenna system.  You could go with a
simple groundplane, which, for the marine frequencies will have about an
18" radiator and four 18" radials.  This will be a "unit" gain antenna
but a substantial improvement over the portable radio antenna.  Next
consideration is the feedline going from the radio to the antenna.  You
will want to keep it as short as possible/practical.  Unless your
feedline length is 20 feet or less, I would stay away from the RG58
mobile type coax.  This is the stuff a little smaller in diameter than a
pencil.  Any coax run longer than 20 ft, I would recommend RG8 or RG8AU.
 Even then I would try and keep the coax run under 100 ft.

You will want your antenna up has high as possible, in the clear,
especially in the direction you wish to listen.

Antennas come in all sorts of sizes and shapes.  As I mentioned, a
simple groundplane is small, simple, "0" gain, relatively inexpensive
and easy to install.  Larger antennas offer gain, but sacrifice size,
cost and ease of mounting.  If all you are going to do is listen, you
could install a beam antenna, which will offer significant signal gain,
but only in the direction in which you point it.

I am not sure, but I think beam antennas are prohibited on the maritime
frequencies.  I know they are prohibited on vessels and they may be
prohibited on fixed stations to, but then again, if all you are doing is
listening, that point is irrelevant.

With a good receiver, decent antenna system, and an unobstructed signal
path to the sea, you could easily be listening to vessels 30-50 miles
out to sea.

An external antenna and a linear amp is the way to go, you can get 250 (or
2000) watts that way.

It's pretty much that simple.  There are a few problems, however:
1. You're not going to be doing it while on bedrest.
2. Most antennas do not come with the connection for the handheld installed.
They do that to make it easy to run the wire.  You have to get the connector
on just right, with a good ground and no shorts, or you're not going to like
the results.
3. VHF is line of sight.  You're going to have to get the antenna high to
improve your reception much.
4. It's going to cost about $100 in materials alone.
5. You can legally listen to whatever you want, but you may not be able to
legally broadcast.

Suggestion, get one of the many radios designed to pick up a wide range of
signals, from aircraft, to marine, to race car, to police, etc.  With a bit
of shopping, you can probably find one for less than it will cost you to
have a quality marine antenna installed.

Lee