One thing I noticed very quickly when I first started training with swords was how rapidly my arms and shoulders wore out and became too fatigued to safely or successfully execute any fencing techniques.
(Quick background: when I was in Uni, I was quite weak in the torso and arms due to malnutrition, although my legs were fairly reliable from several years of lengthy walks and bicycle rides)
Now, whether one trains with a HEMA group or a re-enactment group, chances are you generally don't spend enough time in class each week to develop the requisite strength quickly. At least, such was the case for me.
Now, you could go to the gym, true, but you may not have the time, money and/or inclination to do so. Personally, I prefer a method which is cheap and doesn't require me to leave home.
The method I ended up going with is simply this: Handweights.
Pop down to your local Sports Equipment Store (eg. Rebel Sports) and fork out between 5-15$ for a couple of light handweights.
Ideally, you'd want 2 of the 1.5kg or 2kg weights - however, if at this time you are having difficulty holding a rapier in extended guard for more than a minute, then start with the 1kg weights, but get the 1.5kg ones as well (which you can use to test how far your strength is coming along).
1 - The Spanish Guard
This exercise is ideal for getting used to having your sword arm extended in guard for lengthy periods. You can do this while standing in front of the television, or at any time when your mind is otherwise engaged but your body and arms are doing nothing of use.
Simply hold the weight in your hand like you would a rapier's grip, feet approximately shoulders width wide, and hold your arm at length (as per image to the right). Do not lock in your elbow.
Periodically change your hand position from fingernails facing down, to fingernails facing to the inside, and then with fingernails facing up. When one arm gets too tired, swap arms.
(Image from Pacheco's The Book of the Greatness of the Sword (1600) with thanks to the hard work of Mary and Puck Curtis)
2 - The Cuts
Now, simply holding your arm out with weight in hand isn't going to work all of the required arm and shoulder muscles. So, when boredom with the first exercise sets in (and it will, trust me!), switch over to this one.
This exercise is fairly intuitive for anyone who has watched any swashbuckling movies (Pirates of the Caribbean included). Without damaging your household or those you may live with, perform a sequence of cuts with arm extended and weight in hand.
NB: Do not lock the elbow in, but make sure that at the point where you imagine the cut has 'connected' your arm should be almost straight if you want to be working the arm and shoulder well. Remember you can cut with finesse and panache using movements of the wrist and elbow. Not every strike has to be a 'Conan Special'.
3 - The Guards
This exercise presumes that you have been taught a range of wards and guards for your particular style of bladework.
This exercise simply consists of moving from one guard/ward to the next with the weight in hand. Try different speeds, ranging from slow and deliberate to fast (but only as fast as you can maintain the correct guard position). Make sure you hold your arm in the guard/ward position for at least 5-10 seconds. Make sure that, at some point, you hold each guard for a lengthy position, as you did in Exercise 1 - The Spanish Guard.
HOW TO GAUGE PROGRESS and push it forward more.
This is relatively simple to do - all you need is a timer of some form.
Let us assume for arguments sake that you started with a 1kg handweight, and could only have it extended in the Spanish Guard for 1 minute before you had to drop your arm.
Every time you subsequently hold the guard for longer than 1 minute is a sign of improvement.
When you can hold it for 5 minutes or more at the current weight, increase the weight (to 1.5kg, for this example).
You will find that you may once again only be able to hold the new weight for around a minute or so. However, when your arm gets too tired for the 1.5kg weight, change it immediately to the 1kg (without taking a break). You should find that you will be able to continue the exercise for a couple more minutes.
As time progresses you will find in much the way that I have, that when you pick up the rapier at training or in the fighting lists, your arm will not tire out so quickly and you will be able to get in a lot more quality fencing for your time and effort.