As an Orc who specializes in 1H / Block I've had quite a bit of success with melee combat. Against Dragons however I find it to be pretty hit or miss. Presumably the strategy when engaging them at melee range would be to power bash frequently, allowing you to land valuable shots while preventing them from attacking. For me however there seems to be very little consistency as far as when my power bashes actually cause them to stagger backwards. Sometimes it works as intended, but often times it does nothing and they're able to take huge chunks of my health with their frost / fire breath or bite. I've made sure that I'm not flat out missing them either. I'm definitely connecting, they're just not reacting to it. Am I doing something wrong timing wise? I'm starting to really lose my patience with these dragon fights.

Move around while hitting them and when they are about to breathe fire/frost, go behind them until they stop

actually what you should do is save the bash for when the dragon actually uses a fire/frost breath attack and what I do is move to the side of the dragon to attack. And I wouldn't recommend going behind because the tail does more damage than the breath. Use the bash when he fires or frost breaths use, otherwise attack with the 1 hand.

When i fight them on my orc warrior with 1 hand and block i try to keep my stam up, dont bash at all or power attack unless they breath, try to block there bites but dont bash them. I only play on adept but it works pretty good for me.

Another thing is play around with enchants, I'm not sure people say resistances are broke but I fight ancient dragons on expert with no problem.

Hmm, so the prevailing idea here seems to be that I need to wait until their breath attack. Perhaps then I was doing it too early. If I wait until they breathe on me I'll end up taking damage, but if it's not significant AND it allows me to actually stun them that would be awesome, and more or less what I was looking to do all along.

One of the absolute most awesome things for going up against Dragons as a 1H+Shield user, is Spellbreaker. Check this out. http://www.youtube.com/watch?v=59kT-gD9US0

Use some frost resist gear, it'll be easy.

Use the bash as an interrupt, save it for when it breathes. Firebreath and unrelenting force can also be used. Get health absorb on weapon and fill it up just before the fight. Have health and stam pots favourited and just use Q as a pause where you can heal to full if you need to.

If you have restoration, you can often run away using line of sight and heal up and start again. Fighting around a big treestump for example, has a bit of comedyvalue, and works well.

And yes, resist gear and resist pots.

Ah, will definitely be getting this right away. Thanks.

Dual weilding with the one handed perk tree maxed out destroys EVERYTHING.

eeehh sword and shield vs. dragons is the easiest way to kill them.... needs 0 tactic. just powerbash and hit... you don't need to move at all... why move to the side or to the back? if he breaths just one bash and it's over

try the side, seems like dragons have a hard time hitting you there, Also down some resist potions

I play a 2-hander (who's an Argonian, so by no means optimized) and find that if I can get close, the dragon is toast. I do try in come in at the side, and I use the best (self made) 2 handed sword I can, throw out the "Elementel Fury" shout, and do standing power strikes (with perk) as fast as a can. They don't last long, and I rarely get hurt (that happens while I'm waiting for them to land... I usually get hit by a blast or two, but I try to dodge)
Before I had "Elemental Fury" I carried around a frost enchanted greatsword, because the lower level dragons are mostly fire breathers, and have 75% vulnerability to frost. As a one handed weapon & shield user, maybe you can afford to carry both a frost and flame blade. I don;t bother with weapon enchantments any more, since you can't use Elemental Fury if you are holding an enchanted weapon. I do still use a fire / frost based ranged weapon (depending on the dragon) to force landings.