I'm going to start my answer by clarifying a few of your statements: how chivalric are the knights in question, what period of the medieval era are we talking about, what region of Europe, what is a "medieval knight", what do we mean by 'honourable', and the context of the fight.

Firstly; how chivalric are these knights, and what does chivalry mean to them? First things first, we need to acknowledge the fact that, more often than not, Knights were not very good at sticking to whatever chivalric code they acknowledged when push came to shove. We have many primary source accounts that describe the lassitude of knights towards their chivalric obligations... and far fewer of those knights who stuck to their chivalric guns (or arming swords) to the bitter end. (The only historical example I can think of of the classical 'chivalrous knightly combat' are accounts of The Combat of the Thirty.)

The more closely we look into history, the more clearly shall we perceive that the system of chivalry is an invention almost entirely poetical... It is always represented as distant from us both in time and place, and whilst the contemporary historians give us a clear, detailed, and complete account of the vices of the court and the great, of the ferocity or corruption of the nobles, and of the servility of the people, we are astonished to find the poets, after a long lapse of time, adorning the very same ages with the most splendid fictions of grace, virtue, and loyalty.

Jean Charles Leonard de Sismondi (1885-88), Historical View of the Literatures of the South of Europe, p.79.

We also need to note that the basic code of chivalry is, largely, an informal code - and is not clearly defined in any sense. Rather, our notions of chivalry are a Frankenstein of three primary source accounts (Ordene de chevalerie, anonymous, ~1220. Libre del ordre de cavayleria, Ramon Llull, ~1270. Livre de Chevalerie, Geoffroi de Charny, ~1340) combined with later clarification by scholars who attempted to codify the concept when, really, it had never been. (Leon Gautier, '10 Chivalric Commandments', which he laid out in Chivalry, 1891.) So what are the particular chivalric values these knights hold too? Let's assume that these knights follow the virtues that are most popularly described as chivalric in primary sources - faith, service, prowess, courage/valour/elan, fairness, mercy - and are paragons of chivalric virtue. (An almost mythic concept.)

There's an instinct in popular history to bucket all of medieval Europe together both in space and time. This couldn't be further from the truth: Europe was a melting pot of countless cultures and traditions, and even shared trans-cultural beliefs like 'chivalry' were often interpreted very differently 'the next town over'. So let's assume the fight in question is occurring in a region and time that conforms well to the popular perceptions of knighthood, chivalry, and knightly duels: the early 14th century in northern France.

Now, let's define a knight. This may seem pedantry, but what is defined as a "knight" has a pretty wide range and has undergone multiple shifts throughout the centuries. While previously a Knight was essentially just a military office granted by a lord generally associated with mounted, armoured, warriors - by this time the idea of a knight had clarified into a noble rank with an associated privilege, closely tied to the chivalric code of honour. Are the knights in question a member of an Order of Chivalry/Monastic Order such as the Order of the Holy Ghost? This could effect their approach to the situation. Are the knights in question bachelors (fighting under another's banner) or bannerets (fighting for themselves) - and do they hold other titles? The questions of surrender and responsibility become much greater when your death could lead to disputes of land, or title. Lets keep it as simple as possible by assuming these two knights are bannerets with only minor land holdings and have no other titles and have taken no orders.

"Honourable" was actually a fairly malleable concept, and varied greatly by context and circumstance. What was honourable in times of peace often wasn't during times of war. Additionally - conduct that would be considered reasonable in a duel of justice or honour would probably not be so acceptable during a chivalric hastilude (a martial game). But you've specified this fight is for risk of capture and ransom, which implies wartime conditions; so let us say this duel is occurring "on the field"; and there are no urgent orders or objectives to pursue during the battle asides from pummelling each other into submission. ( Clifford J. Rogers, Kelly DeVries and John Franc. Journal of Medieval Military History: Volumes VII-VIII)

Finally, we have to consider how they were fighting. Primarily: is this duel on horseback, or on foot - and how formalized is the duel in question? Have conditions been set and agreed upon (as was the most common case for formal duels)? I'm going to assume this fight - being, as implied, a wartime affair - was unconditional... as otherwise the question would be a very easy one to answer: "whatever the terms under the conditions of the duel allow". I'm also going to assume the fight is, as would be the most common situation in wartime, on horseback but could very well end on the ground.

Now we can actually start to answer the initial question with all of our clarifications in place. May the fight between our two hypothetical chivalric knights at war in 14th century northern France commence!

Citations for the following are:

- Clifford J. Rogers, Kelly DeVries and John Franc. Journal of Medieval Military History: Volumes VI-VIII

- John Ellis. Cavalry: The History of Mounted Warfare.

- Ken Mondschein. The Knightly Art of Battle

- Dierk Hagedorn, Bartlomiej Walczak. Gladiatoria: Medieval Armoured Combat – The 1450 Fencing Manuscript

The fight is likely to start with lance passes, which was considered the best way to open a fight on horseback. And it is here we would see the first reasonable point of surrender; whichever knight was dismounted, broke their lance, lost their shield, or was otherwise disadvantaged at this point would be in a very reasonable position to surrender! This isn't a game; and if neither opponent wants the fight to end in a death, they'd best end it as soon as possible. Even a couple of tilts would be considered a suitable display of valour by most accounts; it isn't easy to charge headfirst into the tip of an approaching 9.8-foot long reinforced wooden spike aimed towards your heart or head! So if both knights survive this phase of the battle, and one has been clearly bested surrender would be appropriate.

But if for whatever reason, the knights either didn't begin with lances, or both lost the ability to attempt to impale each other from a safe distance - they would begin trying to impale each other from an unsafe distance. Melees, were messy, dangerous, brutal affairs. This phase of the fight would generally involve trying to dismount the opponent. Killing an enemy in full plate is difficult at the best of times: far more so when you're both on horse. Generally, a knight would be dismounted in melee well before they were killed or captured. Dismounting generally happened quickly once a melee commenced, and this would be a likely point of surrender - fighting someone on horseback when you are not is an immense disadvantage, and only an exceedingly brave individual would attempt it if they had surrender and survival in mind. Beyond that; forceful dismounting often caused injury.

Finally, somehow, both knights have wound up without a horse and still wanting to tussle. If medieval fighting manuals are any indication, fights of this fashion assumed both opponents were going to at least be trying to kill each other. There's not much mention of techniques that were designed to subdue. But these are very chivalric knights, neither of whom have blood on their mind. We'd expect one of a few things to provoke a surrender here; a disarming, a wound, exhaustion, an overturning (obviously outmatched or placed in an unwinnable position), or a pin. Generally, if you could do one of these things you have displayed enough of a differential in skill (or luck), that there is nothing more to prove. Someone who wanted to surrender would have no reason to keep fighting at this point if they had a reasonable expectation that it would be accepted. Remember; there is no defined 'point of surrender' in most chivalric codes... you simply have to have shown sufficient valour, and a chivalrous opponent is expected to be merciful.

As for what surrender would look like? You can't really 'choose' how you'd surrender in most circumstances; trying to clearly annunciate anything but a grunting plea when you are exhausted and pinned under the weight of a full grown knight in heavy Armor with a knife trying to find gaps in your armour would be quite a challenge. Since there is no formalized conduct as to how to surrender in most chivalric writing, we can assume the expectation was: however you can.