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So, I managed to get a Kerbal stranded in a nasty orbit. I burned out of a moon mission with bingo fuel and chose too high a periapse; it was just within Kerbin's atmosphere but it was high enough that after a few successive orbits my apoapse was still inside the Mun's SOI. I was warping aggressively and ended up accidentally getting a Munar slingshot that put me in a highly inclined, highly eccentric orbit without enough monopropellant or bipropellant to get back to an aerobraking trajectory. Worst of all, it was a powered lander, so I didn't even have a chute to use even if I'd been able to EVA-push the ship into an aerobraking trajectory. Of course, I could have just terminated the vessel, but I didn't really want to. So I needed a rescue mission. At this point, I'd never done even a single orbital rendezvous (not with another spacecraft, that is), let alone a highly inclined, highly eccentric orbit with a dead target. This was tricky. I couldn't really find any specific set of instructions, so I figured it out as I went along, and figured that someone else might also be interested in them. Step 0: dV for days You're going to need a lot of fuel to pull this off, so for the love of Kraken use a large launch vehicle with a hefty amount of bipropellant for orbital maneuvers. There are ways of doing this that are slightly more efficient, but they aren't nearly as straightforward, so just plan for extra Step 1: Match inclination It's really dV-costly to change inclination once you're already in orbit, so wait until KSC passes directly under the orbital path of your target and then launch either North or South, depending on the angle of your target. Go to map view and set your target as target so that you know the inclination of the descending and ascending nodes, and vary your launch direction in order to keep this value to a minimum. Once you're in orbit, use a normal or antinormal burn at the ascending or descending node to zero out inclination difference. Step 3: Circular intercept To have any chance of intercepting your target, you need to be in a circular orbit that touches the orbit of your target. The most efficient way to do this is to touch the orbit at your target's nearest approach to Kerbin, its periapse. So write down that altitude, then burn prograde to raise your apoapse to that altitude. At your apoapse, burn prograde again to circularize to exactly that altitude, so you end up with something like this: Technically, it is more efficient if you are in an eccentric orbit where your apoapse matches the periapse of your target, but this is more difficult to achieve and makes your timing a lot less forgiving. Step 4: Timing the Rendezvous This is the part that confused me, and it took me forever to figure it out. It does no good to match the orbit of your target before the rendezvous. Don't do it. Instead, set up a rendezvous as close as possible to the periapse of your target. Here's the magic. When you are next at the interception point, your target will still be some distance away, with a certain time (2 hours, for example) separating it from that point. You need to burn at that interception point until the total period of your new orbit exactly matches the time separating the target vessel from your current location. This will ensure that you complete your new orbit just in time to meet up with your target at its periapse. Voila! Thankfully, this isn't the 1970s, so you don't have to calculate these periods using Kepler's Laws. You can simply place a maneuvering node at the interception point and drag it prograde until the "closest approach" markers line up at the interception point. Make this as precise a match as possible, then go ahead and do your burn when you reach the node. It's a good idea to burn about 90% of the maneuvering node and then delete it and complete the burn manually, since your screen will be less cluttered and you can see the closest approach markers more clearly. You should aim to be within a few kilometers of your target. Step 5: Catching up Once you reach your rendezvous point, switch to targeting mode on your navball, point retrograde (which, in this case, is a relative retrograde), and burn to reduce relative velocity to zero at your nearest approach to your target. You want to be lined up along a radial vector with as little prograde-direction misalignment as possible. You'll probably want to split this into a few burns. Once you've zeroed out relative velocity, you can proceed to approach and dock (or EVA, or whatever) normally; there are plenty of good tutorials for that.