Sometimes it happens. You're traveling (especially as a woman alone, but not exclusively), and you meet a guy. Maybe it's a fun weekend fling, or maybe the interest is more one-sided, but suddenly the topic of marriage comes up. Usually prefaced by one of these subtle questions...
"Do you think you could ever marry a person from this country?"
"Our skin tones combined would make a gorgeous baby"
"Wouldn't you like stay here and find a local husband?"
Whether your hand is solicited directly or through an intermediary (usually an aunt or grandmother), it's important to deal with the situation appropriately.
In any case, if the proposal is respectful and honest, you should approach the situation with equal respect along with cultural sensitivity.
So let's swallow our ethnocentric impulses and try to put ourselves in someone else's shoes.
Of course, an appropriate reaction depends on the proposal...if it's mostly a joke, you might be able to just laugh it off. If it's aggressive or threatening, or you feel uncomfortable or in danger (say, your taxi driver keeps pulling over on a deserted highway to beg you to marry him), then you need to be prepared to get the hell out of there.
Regardless of whether you want to marry the person, or what reasons you have, the first thing that will likely come to your mind is "that's crazy!"
While in Western European/American cultures, such a proposal may in fact be crazy, it is only so because it runs counter to cultural expectations and norms. There's nothing inherently crazy about the idea, is there? Take yourself out of your cultural context. Apart from the "weird" factor, which comes mainly from what experiences you already have had and what expectations they've built, what are the actual reasons you are not interested in marrying this person?
If You Don't Want to Marry Them...
Think of the real, deep reasons why you don't want to accept the proposal.
Don't make excuses that aren't true, unless they won't accept your refusal.
Resist your first impulse to say "no, that's crazy!" because it sounds so different than any experience you've so far had or seen.
Accept the cultural differences that have led to this situation, try to understand the proposer's desires and reasoning.
Explain calmly and clearly why you are not interested in the proposal, without being condescending or judgmental.
Try to not let the proposal affect the way you think of and respect this person, if your prior relationship was otherwise positive.
Don't back down from your decision because you feel bad for them.
If they are interested in marriage as a way to move them out of a negative situation in their home country, suggest other ways you'd be willing to help, like helping them apply for a green card
If you're certain of your decision, don't make it seem like you're not by saying things like "maybe in a year or so" or "let's talk about this later"- it will only build a false hope and make it more difficult for both of you in the future.
If You Do Want to Marry Them...
Think of your relationship out of the context of your current location or trip- are you getting caught up in the romance and excitement or could this relationship really stand on its own?
Think of (and discuss) the practicalities: where will you live? What kind of work will you do? Do you share the same cultural values? Do you share the same vision for what your life will look like in 5 years? In 50? (consider the story of "The White Massai"- Corinne Hofmann)
On a Personal Note...
I have been proposed to a few times, and interest has been hinted at innumerably. A favorite line of questioning in Georgia goes:
"Do you like Georgia? Do you like Georgian food? Are you married? You can stay here! I have a son/nephew/cousin/friend you can marry!"
I was proposed to by a Chechen man who already had one wife...he then proceeded to tell me how beautiful I would look in a hijab.
I was proposed to by the sweetest, most sincere and emotional Chechen body builder- he offered to wash dishes and cook even though it's a shame for men to do those things in Chechen culture, because I had such a "beautiful smile"
I was proposed to by a man who speaks barely any Russian and no English, through three women who served as translators and character witnesses for him. When I declined, he said he'd be willing to just get married on paper for now so he can come to America, and then he would just wait for me to be ready to marry him for real.