How does a baptismal certificate work? Why do you even need a certificate? Would other churches disqualify your baptism, or disallow you from participating in other sacraments, if you happen to lose your baptismal certificate? Do Christians keep them in safe places in their homes along with their birth certificates, passports, Visas, social security numbers, and other important documents?
Baptismal certificates are still used by Churches for whom Trinitarian baptism is important. This is so that they can be certain that someone has been validly baptised. The Catholic, Anglican and Orthodox Churches recognise each other’s baptisms and those of many other denominations as a valid, once-for-all and transferable sacrament. But it can only be transferable if it can be proved to be so.
When I and others joined the Roman Catholic Church under Anglicanorum Coetibus, we were required to produce evidence of our baptism. I no longer had my certificate, and others were baptised by a Free Church and never given one in the first place.
In my case, the [Anglican] parish church had recorded my baptism in a register, as the Church of England requires. It had since deposited its registers with the local authority archive, and they had scanned them and made them available online. So I could easily get a copy of the register entry, and the Catholic Church was satisfied that I had been baptised using a valid Trinitarian formula.1
Others were not so fortunate, and on joining the Catholic Church had to be baptised by that Church. This was so that the Church could be satisfied that they had been validly baptised: if any previous baptism had been valid, doing it again would make no difference; and if not, then they’d be doing it for the first time.
Certificates of baptism do still have uses within the Christian Church.
1 When I was a churchwarden, I used to do similar searches of registers we held in the parish for those who had been baptised at the church and now wished to marry in the Catholic Church, or even be confirmed in the Church of England.
Many years ago, before governments were in the habit of providing live birth documentation and proof of identity, a baptismal certificate was valid proof of citizenship. Because people didn't move around, churches took upon themselves the responsibility to know the souls in their area, and kept register of the same. For the previous generation, where not everyone had identity documents, these could be used in lieu of a birth certificate - although usually now they are only accepted if the birth certificate cannot be located. Technically even today, the State Department will accept it as secondary evidence of citizenship, but it is rarely used.
That said, once the church ceased to be the primary social force within communities, the identity management role fell away. Governments took over the role of maintaining registers on people, and the baptismal certificate is now mostly a relic. The "keepsake" is now pretty much just that - a document that serves the function of reminder, but has little practical value. As a practical matter, churches are allowed to create baptismal certificates in any manner they see fit. And yes, that usually means some sort of nice drawing program or a word processor with clip art nowadays.
Back when churches were very picky about who would be allowed to be a member, they might require proof of baptism. Nowadays, when a person joins a church, the pastor typically just takes their word for as to whether or not they are baptised. In some instances, when a membership is transferred, the pastor may contact the previous church, to inquire about records, but it is for all practical purposes, just a formality.
And, if you want my experience - no, I do not have my baptismal certificate. Some people do, I don't. Nobody cares about, and I've never seen one hanging in the way a diploma is.