Consider how much time has passed. Dating a widower whose spouse has recently died could be a lot more complicated than dating someone who has put time and distance between the event and you. If the death is more recent, or if you sense there's little resolution even with the passage of time, be more cautious.
Take into consideration the age of your new object of your affection. A man who lost his wife at a young age will be facing different issues than an older man who may have expected the passing on some level. Along with this issue, weigh in how his wife died. Was it sudden or after a long illness? All of these aspects affect how far along he may be in moving forward with his life and being ready to give his heart to you.
Notice if you are a carbon copy of his former wife. If your boyfriend is still heartbroken and trying to recapture what he had with his wife, he may look for a woman who is exactly like his former spouse. When you look at pictures of his wife or hear descriptions and you think she's eerily similar to yourself, proceed with caution.
Look for signs that he has emotionally moved on. Losing anyone important to you is devastating and takes time to get over. It may even take a lifetime to ever fully move on. Still, when a boyfriend is ready, he will remember her more fondly rather than always be saddened by her memory. You can help him deal with this loss by being patient and supportive during the rough times.
Cut him extra slack when he's reminded of a special memory. Certain times of the year or places will bring back emotions for your boyfriend. Try to give him space during these times and don't judge him too harshly. Likely he will return to you after a period of time and appreciate you even more because of your patience.
Suggest you see a counselor together when you start to get serious. There will likely be issues too difficult for you to face on your own as you approach the idea of marriage and your partner is reminded even more of his loss. It may only take a few sessions to get on the right track but it's better to give your transition the best foundation.