If a car seat is not available, what is the safest way to secure a child in a car?

Buy a car seat; it's the law. http://www.ghsa.org/html/stateinfo/laws/childsafety_laws.html

My understanding is that if it's absolutely necessary, you should always sit in the back with the child on your lap but not inside the seatbelt with you - in an accident, the child will be crushed between you and the belt. If you sit in the front seat, in an accident the child will go through the wind screen. You should also make sure you sit behind one of the seats not behind the gap between front bucket seats. In the event of any but the most gentle bumper bender, you will lose hold of the child and it will likely go through the windscreen.

Neither.  Put that kid in a car seat, pronto. Child being held by adult runs a risk of being ejected upon collision when adult is restrained and child is not, making child a projectile. Child being partially restrained by a shoulder strap in the wrong position runs the risk of head/neck/shoulder injuries on collision.  Not to mention partial or complete decapitation if you are very unlucky. Even on airlines they have an extension of the adult's belt for lap sitting kids. Seriously, you only have to be involved with or witness the aftermath of an accident involving a child not properly restrained one time to develop a deep and passionate commitment to child safety seats.

If the child is sized like a 4-5 year old, they can (in an utter emergency, where if you get pulled over you WILL get an expensive ticket) ride in an ordinary seat belt, properly adjusted, and it will be as safe as the lowest-end carseats on the market. The Freakonomics guys actually crash-tested a standard set of seatbelts on an apparatus intended to certify carseats, and the results were in the certifyable range. Which means there can be carseats legally sold in the US that protect children only as well as an ordinary lap-and-shoulder seat belt, with no adjuster or tensioner or positioner: http://freakonomics.com/2005/07/10/freakonomics-in-the-times-magazine-the-seat-belt-solution/ http://freakonomics.com/2005/07/09/more-evidence-on-car-seats-vs-seat-belts/ Which doesn't make it legal or the VERY SAFEST option; in fact, a well-padded fitted crash-couch with five-point restraints, rear-facing, is the safest option for ANY age of passenger if you happen to get in a crash. It just shows that the car-seat-manufacturer lobby has done a good job of throwing money behind the occasional bereaved parent and gotten their products legally required far past the age when they are the ONLY possible safe answer.

Do you mean  while driving in a car? Get a car seat  suitable for the child's size and body weight. Most hospitals in the US will not let you leave the premises with a baby unless they verify you have a car seat. They also lend you one -on the spot - if you don't have it. A unrestrained child held in your arms in a rear end collision will either be forced from your arms and act as a  missile to be flung against the next solid surface. That could be the glass windshield, the dash board or the back of the seat  in front of you Seat belts are designed to automatically tighten when there is an impact. On a grown person the rib cage is sufficient to interact with the belt during a collision. A child's bone structure is not strong enough  to withstand that and his chest will be crushed. The same goes for small dogs that people put on their laps when driving. Here is a link to a condition called flail chest which is what happens when a person is not properly restrained. These are words. I didn't pull the images. http://en.wikipedia.org/wiki/Flail_chest If you have a car and a toddler put down the keyboard and get a car seat. Now.

It is actually illegal in the US to do either. But to answer the question as written (no car seat), it is better to carry the child with the seat belt around the adult with the child being held. It would be somewhat similar to oxygen masks coming down on an airplane. The adult should first strap his on, then put one on the child.This answer is not a substitute for professional medical advic...

There is no "safe" substitute. If you are in the US it is the law. Besides that if it is your child why would you put their life at risk?  If it's not your child you have no business making a decision to take a child in a car with out adequate safety equipment (even if it is your child. ) Break down and buy one, and never buy a used one!

The question asked for the safest way to secure a child in a car without a car seat, not whether or not that action is legal.  The answer is in the back seat with a seatbelt for that child, not in the lap of an adult.  Below is a link with some of the only (relatively) recent crash-test research for children not in car seats.  This was very controversial when it came out and a number of flaws have been identified with the accompanying research, which drew from crash data sets.  Disappointingly, little follow-up crash test research has been conducted.  Don't read half of this article and skip the end- the authors include important notes on what conclusions should and should not be taken from the research.  Important among those is that a car seat should be used in areas where legally required. http://www.nytimes.com/2005/07/10/magazine/10FREAK.html?pagewanted=1&_r=3&ei=5070&en=641c83d4b0668293&ex=1189915200&

They all suck, and if there's a problem, it won't matter. You'll hate yourself for not buying a car seat and using it properly. I'm not even going to comment on which is the safer of the two alternatives, because they're both illegal in the United States.